Battery system for secondary battery comprising blended cathode material, and apparatus and method for managing the same

ABSTRACT

Disclosed is a battery system for a secondary battery including a blended cathode material, and an apparatus and method for managing a secondary battery having a blended cathode material. The blended cathode material includes at least a first cathode material and a second cathode material. The first and second cathode materials have different operating voltage ranges. When the secondary battery comes to an idle state or a no-load state, the battery system detects a voltage relaxation occurring by the transfer of operating ions between the first and second cathode materials.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of co-pending application Ser.No. 13/969,128 filed on Aug. 16, 2013, which is a continuation ofInternational Application No. PCT/KR2013/002149 filed on Mar. 15, 2013,which claims priority to Korean Patent Application No. 10-2012-0038779and 10-2013-0028120 filed in the Republic of Korea on Apr. 13, 2012 andMar. 15, 2013, respectively, the disclosures of which are incorporatedherein by reference.

TECHNICAL FIELD

The present disclosure relates to a battery system for a secondarybattery comprising a blended cathode material, and an apparatus andmethod for managing a secondary battery having a blended cathodematerial.

BACKGROUND ART

A battery generates electric energy by oxidation and reduction reactionsand is widely used in various ways. For example, a battery is applied toportable devices such as cellular phones, laptops, digital cameras,video cameras, tablet computers, and electric tools; electric-drivenapparatuses such as electric bikes, motor cycles, electric vehicles,hybrid vehicles, electric ships, and electric airplanes; power storagedevices used for storing power generated by new regeneration energy orsurplus energy; uninterrupted power supplies for stably supplying powerto various information communication devices such as server computersand base stations for communication, and so on.

A battery includes three basic components: an anode containing materialwhich is oxidized while emitting electrons during discharge, a cathodecontaining material which is reduced while accepting electrons duringdischarge, and an electrolyte allowing the transfer of operating ionsbetween the anode and the cathode.

Batteries may be classified into primary batteries which are notreusable after discharge, and secondary batteries which allow repeatedcharge and discharge since their electrochemical reaction is at leastpartially reversible.

The secondary batteries include lead-acid batteries, nickel-cadmiumbatteries, nickel-zinc batteries, nickel-iron batteries, silver oxidebatteries, nickel metal hydride batteries, zinc-manganese oxidebatteries, zinc-bromide batteries, metal-air batteries, lithiumsecondary batteries and so on, as well known in the art. Among them,lithium secondary batteries are drawing the most attention due to theirhigh energy density, high battery voltage and long life cycle incomparison to other secondary batteries.

The lithium secondary battery has a distinctive feature in thatintercalating and deintercalating reactions of lithium ions occur at acathode and an anode, respectively. In other words, during discharge,lithium ions are deintercalated from the anode material included in theanode, transferred to the cathode through an electrolyte, andintercalated into the cathode material included in the cathode. Duringcharging, the above processes are performed in reverse order.

In the lithium secondary battery, since the material used as the cathodematerial greatly influences the performance of the secondary battery,various attempts are being made to provide cathode materials having lowproduction costs and large energy capacity while maintaininghigh-temperature stability.

DISCLOSURE Technical Problem

The present disclosure is designed to solve the problems of the priorart, and therefore the present disclosure is directed to revealing anelectrochemical reaction mechanism of a blended cathode material whichmay remedy shortcomings of individual cathode materials by blending atleast two kinds of cathode materials.

The present disclosure is also directed to providing a system, apparatusand method, which allows reliable prediction of electrochemicalbehaviors of the secondary battery containing the blended cathodematerial by revealing the electrochemical reaction mechanism of theblended cathode material to the level of mathematical modeling.

Technical Solution

In the present disclosure, a blended cathode material includes at leasta first cathode material and a second cathode material which havedifferent operating voltage ranges. The first and second cathodematerials have different concentrations of operating ions reactingtherewith according to the change of voltage and allow voltagerelaxation by transferring the operating ions between the first andsecond cathode materials when coming to an idle state or a no-load statein an intrinsic voltage range. The blended cathode material may be usedas a cathode material of a secondary battery which is charged ordischarged in a voltage range including the intrinsic voltage range.

Here, the operating ions mean ions performing an electrochemicalreaction with the first and second cathode materials when a secondarybattery having the blended cathode material is being charged ordischarged. The operating ions may vary depending on the kind of thesecondary battery. For example, the operating ions may be lithium ionsin the case of a lithium secondary battery.

The electrochemical reaction includes oxidation and reduction reactionsof the first and second cathode materials accompanied with charging ordischarging of the secondary battery and may vary according to anoperating mechanism of the secondary battery. In an embodiment, theelectrochemical reaction may mean that operating ions are intercalatedinto or deintercalated from the first cathode material and/or the secondcathode material. In this case, the concentration of operating ionsintercalated into the first and second cathode materials or theconcentration of operating ions deintercalated from the first and secondcathode materials may vary according to the change of voltage of thesecondary battery. In other words, the first and second cathodematerials have different operating voltage ranges as to the operatingions. For example, under the condition where the secondary battery isdischarged, at a certain voltage range, operating ions may bepreferentially intercalated into the first cathode material rather thanthe second cathode material, and at another voltage range, it may be theopposite. As another example, under the condition where the secondarybattery is charged, at a certain voltage range, operating ions may bepreferentially deintercalated from the second cathode material ratherthan the first cathode material, and at another voltage range, it may bethe opposite.

The above idle state means a state in which a high discharge current isdrawn from a secondary battery toward a main load of equipment on whichthe secondary battery is loaded is interrupted, and a minimal dischargecurrent required for an electronic device included in the equipment isdrawn from the secondary battery. If the secondary battery comes to anidle state, the discharge current drawn from the secondary battery isvery low. When the secondary battery comes to an idle state, themagnitude of the current drawn from the secondary battery may beconstant, substantially constant or variable.

For example, the idle state may refer to cases in which (i) a smalldischarge current is supplied to a computer unit or an audio instrumentloaded in an electric vehicle, even though the secondary battery doesnot supply a discharge current to a motor just after a driver starts theelectric vehicle, when a secondary battery is loaded in the electricvehicle; (ii) a driver driving an electric vehicle momentarily stops theelectric vehicle at a traffic signal or parks the electric vehicle at aparking lot; (iii) a processor of the information communication deviceshifts to a sleep mode in order to save energy when an informationcommunication device on which a secondary battery is loaded does notoperate for a predetermined time without turning off.

The no-load state means a state in which the capacity of the secondarybattery does not substantially change since the secondary battery stopscharging or discharging.

The voltage relaxation means a phenomenon in which a potentialdifference is generated between the first and second cathode materialswhen the secondary battery comes to an idle state or a no-load state,where the potential differences cause the transfer of operating ionsbetween the cathode materials so that the potential difference decreasesas time passes.

Here, the voltage relaxation occurs when the secondary battery includingthe blended cathode material and being discharged in the intrinsicvoltage range shifts to an idle state or a no-load state. If thesecondary battery is discharged in the intrinsic voltage range, amongthe first and second cathode materials, the reaction capacity of thecathode material that more preferentially reacts with operating ionsbecome almost exhausted, and so the other cathode material starts toreact with the operating ions.

Under this condition, if the secondary battery shifts to an idle stateor a no-load state, operating ions present near the surfaces of thefirst cathode material and the second cathode material are diffusedtoward the center of the corresponding cathode material at variousdiffusion speeds, thereby generating a potential difference between thecathode materials. The generated potential difference causes thetransfer of operating ions between the cathode materials and as a resultbrings a voltage relaxation which eliminates the potential difference ofthe cathode materials.

Considering the phenomenon of the voltage relaxation, the idle state orthe no-load state may also be defined by the following viewpoint. Inother words, if a discharge current is drawn from a secondary battery,operating ions are intercalated into the cathode materials. However, ifthe magnitude of the discharge current is sufficiently small, eventhough operating ions are intercalated into the cathode materials, thetransfer of the operating ions between the cathode materials for thevoltage relaxation may maintain. Therefore, a state in which the flow ofa small discharge current does not disturb the occurrence of a voltagerelaxation between cathode materials and a state in which a dischargecurrent does not flow may be defined as an idle state or a no-loadstate, respectively.

In one embodiment, when the secondary battery comes to an idle state ora no-load state, a small current less than 1 c-rate may be drawn fromthe secondary battery.

In another embodiment, when the secondary battery comes to an idle stateor a no-load state, a small current less than 0.5 c-rate may be drawnfrom the secondary battery.

In still another embodiment, when the secondary battery comes to an idlestate or a no-load state, a small current less than 0.1 c-rate may bedrawn from the secondary battery.

The magnitude of the small current drawn from the secondary battery mayvary according to the kind of a device on which the secondary battery isloaded. For example, in the case the secondary battery is loaded on ahybrid or plugged hybrid vehicle (HEV or PHEV), the c-rate is relativelyhigh, while in the case the secondary battery is loaded on an electricvehicle, the c-rate is relatively low.

The intrinsic voltage range may vary according to various factors suchas the kind of first and second cathode materials, the magnitude ofcharge or discharge current of the secondary battery, a state of thesecondary battery when the secondary battery comes to an idle state or ano-load state, or the like.

Here, the ‘state’ of the secondary battery means an amount of availableelectric energy stored in the secondary battery and may be ‘State OfCharge’, without being limited thereto. The State Of Charge is known inthe art as a parameter of SOC, and hereinafter the term ‘state’ means‘State Of Charge or SOC’ unless stated otherwise.

The ‘state’ may express its value quantitatively by using parameters“SOC” and “z”. The SOC parameter is used when expressing the ‘state’ asa percentage value of 0-100%, and the z parameter is used whenexpressing the ‘state’ as a numerical value of 0-1.

The intrinsic voltage range may be expressed as a state of the secondarybattery in view of the doctrine of equivalents. Therefore, if asecondary battery causes voltage relaxation in a specific state range,it is obvious that the secondary battery operating in the state range isoperating in an intrinsic voltage range.

In the present disclosure, the voltage relaxation phenomenon exhibitedby the first and second cathode materials in the intrinsic voltage rangemay occur between the cathode materials satisfying at least one of thefollowing conditions.

For example, the voltage relaxation may occur if, when dQ/dVdistribution of the first and second cathode materials is measured,locations and/or intensities of main peaks exhibited in the dQ/dVdistribution of the cathode materials are different from each other.Here, the dQ/dV distribution, as well known in the art, means capacitycharacteristics of the cathode material in accordance with voltages.Therefore, cathode materials whose main peaks exhibited in the dQ/dVdistribution have different locations and/or different intensities maybe regarded as having different operating voltage ranges. The differencein locations of the main peaks may vary according to the kind of thefirst and second cathode materials, and for example the locations of themain peaks may be different from each other by 0.1 to 4V.

As another example, the voltage relaxation may occur if, when adischarge resistance is measured at SOCs of 0-100% with respect to thesecondary battery including the blended cathode material, a dischargeresistance profile has a convex pattern (so-called a protruding shape).

As another example, the voltage relaxation may occur if, when dischargeresistance of each SOC is measured with respect to the secondary batteryincluding the blended cathode material, a discharge resistance profilehas at least two inflection points before and after the convex pattern.

As another example, the voltage relaxation may occur if the secondarybattery including the blended cathode material has a charge or dischargeprofile with at least one voltage plateau. Here, the voltage plateaumeans a voltage range where an inflection point is present and a voltagechange is so small before and after the inflection point that thevoltage looks substantially constant.

In the present disclosure, materials useable as the first and secondcathode materials are not specially limited if they may cause voltagerelaxation in the intrinsic voltage range.

In an embodiment, the first cathode material may be an alkali metalcompound expressed by a general chemical formula A[A_(x)M_(y)]O_(2+z),wherein A includes at least one of Li, Na and K; M includes at least oneelement selected from the group consisting of Ni, Co, Mn, Ca, Mg, Al,Ti, Si, Fe, Mo, V, Zr, Zn, Cu, Al, Mo, Sc, Zr, Ru and Cr; x≥0, 1≤x+y≤2,−0.1≤z≤2; and x, y, z and stoichiometric coefficients of the componentsincluded in M are selected so that the alkali metal compound maintainselectrical neutrality.

Alternatively, the first cathode material may be an alkali metalcompound expressed by xLiM¹O₂-(1−x)Li₂M²O₃ wherein M¹ includes at leastone element with an average oxidation state of +3; M² includes at leastone element with an average oxidation state of +4; and 0≤x≤1, andselectively coated with a carbon layer, an oxide layer and a fluoridelayer, which is disclosed in U.S. Pat. No. 6,677,082, U.S. Pat. No.6,680,143 or the like.

In another embodiment, and the second cathode material may be lithiummetal phosphate expressed by a general chemical formula Li_(a)M¹_(x)Fe_(1−x)M² _(y)P_(1−y)M³ _(z)O_(4−z), wherein M¹ includes at leastone element selected from the group consisting of Ti, Si, Mn, Co, V, Cr,Mo, Fe, V, Cr, Mo, Ni, Nd, Al, Mg and Al; M² includes at least oneelement selected from the group consisting of As, Sb, Si, Ge, V and S;M³ includes at least one element selected from a halogen groupcontaining F; 0<a≤2, 0≤x≤1, 0≤y<1, 0≤z<1; and a, x, y, z, andstoichiometric coefficients of the components included in M¹ _(x), M²_(y), and M³ _(z), are selected so that the lithium metal phosphatemaintains electrical neutrality, or Li₃M₂(PO₄)₃, wherein M includes atleast one element selected from the group consisting of Ti, Si, Mn, Co,V, Cr, Mo, Ni, Al, Mg and Al.

In another embodiment, the first cathode material may be an alkali metalcompound expressed by Li[Li_(a)Ni_(b)Co_(c)Mn_(d)]O_(2+z) (a≥0;a+b+c+d=1; at least one of b, c and d is not zero; −0.1≤z≤2). Inaddition, the second cathode material may be at least one selected fromthe group consisting of LiFePO₄, LiMn_(x)Fe_(y)PO₄ (0<x+y≤1) andLi₃Fe₂(PO₄)₃.

In another embodiment, the first cathode material and/or the secondcathode material may include a coating layer. The coating layer mayinclude a carbon layer, or an oxide layer or a fluoride layer containingat least one selected from the group consisting of Ti, Si, Mn, Co, V,Cr, Mo, Fe, Ni, Nd, Al, Mg, Al, As, Sb, Si, Ge, V and S.

In the present disclosure, a blending ratio of the first and secondcathode materials may be suitably adjusted according to anelectrochemical design condition considering the use of a secondarybattery to be manufactured, an electrochemical characteristic of cathodematerials required for causing a voltage relaxation between the cathodematerials, an intrinsic voltage range where voltage relaxation occurs,or the like.

In addition, the number of cathode materials capable of being includedin the blended cathode material is not limited to two. In an embodiment,the blended cathode material may include three kinds of cathodematerials different from each other, for example a blended cathodematerial including LiMn₂O₄, Li[Li_(a)Ni_(x)Co_(y)Mn_(z)O₂ [a≥0; x+y+z=1;at least one of x, y and z is not zero] and LiFePO₄. In anotherembodiment, the blended cathode material may have four kinds of cathodematerials different from each other, for example a blended cathodematerial including LiNiO₂, LiMn₂O₄, Li[Li_(a)Ni_(x)Co_(y)Mn_(z)O₂ [a≥0;x+y+z=1; at least one of x, y and z is not zero] and LiFePO₄. Inaddition, in order to improve properties of the blended cathodematerial, other additives such as a conducting agent and a binder may beadded to the blended cathode material without special restriction.Therefore, a blended cathode material including at least two cathodematerials capable of causing voltage relaxation at an idle state or ano-load state in the intrinsic voltage range should be interpreted asbeing within the scope of the present disclosure regardless of thenumber of cathode materials or the presence of other additives, asobvious to those skilled in the art.

The blended cathode material may be used as a cathode material of asecondary battery loaded on various kinds of electric-driven apparatusesdriven by electric energy, and the kind of the electric-driven apparatusis not specially limited.

In an embodiment, the electric-driven apparatus may be a mobile computerdevice such as a cellular phone, a laptop, and a tablet computer; or ahand-held multimedia device such as a digital camera, a video camera,and an audio/video regenerating device.

In another embodiment, the electric-driven apparatus may be anelectric-powered apparatus such as an electric vehicle, a hybridvehicle, an electric bike, a motor cycle, an electric train, an electricship, and an electric airplane; or a motor-mounted power tool such as anelectric drill and an electric grinder.

In another embodiment, the electric-driven apparatus may be a largepower storage device installed at a power grid to store new regenerationenergy or surplus energy, or an uninterrupted power supply for supplyingpower to various information communication devices such as servercomputers and mobile communication devices in times of emergency such asa blackout.

In the present disclosure, the secondary battery may be charged ordischarged in a voltage range including the intrinsic voltage rangewhere the blended cathode material causes voltage relaxation.

The secondary battery may further include an electrolyte havingoperating ions. The electrolyte is not specially limited if it hasoperating ions and may cause an electrochemical oxidation or reductionreaction at the cathode and the anode by means of the operating ions.

The secondary battery may further include a package for sealing thecathode, the anode and the separator. The package is not speciallylimited if it has chemical and physical stability and mechanicaldurability.

The appearance of the secondary battery is determined by the structureof the package. The structure of the package may be selected fromvarious structures known in the art and may have structures such as acylindrical shape, a rectangular shape, a pouch shape, a coin shape orcurved shapes thereof, representatively.

According to the present disclosure, the secondary battery may beelectrically coupled or connected to a control unit which monitors avoltage characteristic exhibited due to the voltage relaxation. Thecontrol unit may detect the occurrence of the voltage relaxation byusing the voltage characteristic and optionally estimate a state of thesecondary battery corresponding to the voltage relaxation.

In one embodiment, after the secondary battery comes to an idle state ora no-load state while being discharged, the control unit may monitorwhether the voltage variance amount of the secondary battery measuredduring a predetermined measurement time belongs to a critical voltagerange which is capable of corresponding to the voltage relaxation. Thecritical voltage range may vary depending on the blended cathodematerial and may be set in the range of 50 to 400 mV, without beinglimited thereto.

If the voltage variance amount belonging to the critical voltage rangeis monitored, the control unit may indirectly detect that the voltagerelaxation occurs in the blended cathode material included in thesecondary battery, and optionally quantitatively estimate the state ofthe secondary battery corresponding to the voltage change of thesecondary battery during the measurement time.

In another embodiment, the control unit may monitor whether aninflection point supporting the voltage relaxation occurs in the voltageprofile measured after the secondary battery comes to an idle state or ano-load state while being discharged, and/or whether the time takenuntil the occurrence of the inflection point belongs to a critical timerange, and/or whether a slope of the voltage profile at the inflectionpoint belongs to a critical slope range.

When the measured voltage profile has an inflection point, the voltageof the secondary battery may exhibit two voltage rises before and afterthe inflection point. In this case, the voltage relaxation may bealternatively called two-stage voltage relaxation.

The control unit may indirectly detect the occurrence of the voltagerelaxation in the blended cathode material included in the secondarybattery and optionally quantitatively estimate a state of the secondarybattery corresponding to the voltage change of the secondary batterymonitored during the measurement time, if the occurrence of aninflection point is detected in the measured voltage profile, whichsupports the occurrence of the voltage relaxation, and/or if a voltageprofile slope at an inflection point belonging to a critical slope rangeand/or an inflection point within a critical time range is detected.

In another embodiment, the control unit may monitor whether at least twovoltage rises are detected before and after an inflection point whichsupports the occurrence of voltage relaxation at the voltage profilemeasured after the secondary battery comes to an idle state or a no-loadstate while being discharged, and/or whether the voltage variance amountcalculated by adding the at least two voltage rises belongs to thecritical voltage range, and/or whether the time taken until theoccurrence of each voltage rise belongs to the critical time range.

In the measured voltage profile, if at least two voltage rises aredetected before and after the inflection point, and/or if the voltagevariance amount calculated by adding the at least two voltage risesbelongs to the critical voltage range, and/or if the time taken untilthe occurrence of each voltage rise belongs to the critical time range,the control unit may indirectly detect that voltage relaxation occurs inthe blended cathode material included in the secondary battery and mayoptionally quantitatively estimate a state of the secondary batterycorresponding to the voltage change of the secondary battery monitoredduring the measurement time.

The control unit may be a battery management system (BMS) which may beelectrically coupled to a secondary battery, or a control elementincluded in the BMS.

The BMS may be interpreted as meaning a typical BMS in the art, but inthe functional point of view, any system capable of performing at leastone function disclosed in this specification may be included in thescope of the BMS.

The present disclosure may also provide a secondary battery managingapparatus which may detect the voltage relaxation, connected or coupledto the secondary battery, and optionally estimate a state of thesecondary battery corresponding to the voltage relaxation.

The secondary battery managing apparatus may include a BMS electricallyconnected to the secondary battery in order to estimate a state of thesecondary battery.

The BMS may include a sensor configured to measure a current and avoltage of the secondary battery during operation of the secondarybattery, and a control unit configured to prepare a voltage profile andoptionally a current profile from the measured current and voltage ofthe secondary battery, detect a voltage relaxation by using the voltageprofile, and optionally estimate a state of the secondary batterycorresponding to the voltage relaxation.

In another embodiment, the BMS may include a sensor configured tomeasure a current and a voltage of the secondary battery duringoperation of the secondary battery, and a control unit configured todetect voltage relaxation of the secondary battery from the change ofthe measured voltage and optionally estimate a state of the secondarybattery corresponding to the voltage relaxation.

The sensor may measure a voltage and a current of the secondary batteryfor a predetermined measurement time when the secondary battery comes toan idle state or a no-load state while being discharged.

Here, the voltage may mean a voltage between the cathode and the anodeof the secondary battery, and the current may mean a discharge currentdrawn from the secondary battery.

The BMS may include a predefined voltage estimating model. The voltageestimating model may be used for estimating a voltage profile of asecondary battery according to time when the secondary battery comes toan idle state or a no-load state while being discharged.

The BMS may include the voltage estimating model as a software algorithmwhich is executable by a processor. For example, the voltage estimatingmodel may be composed with program codes and stored in a memory deviceor executed by the processor.

The control unit may estimate a voltage profile when the secondarybattery is in an idle state or a no-load state, by using the voltageestimating model when the voltage relaxation is detected.

In an embodiment, the voltage estimating model may estimate the voltageprofile according to time by using the discrete time equations below.V _(cell) =V _(cathode) [k]−V _(anode) [k]V _(cathode) [k]=f(V _(c1) [k],V _(c2) [k],i _(cell) [k],R ₀ _(_)_(relax), . . . )V _(anode) [k]=g(V _(a) [k],i _(cell) [k], . . . )V _(c1) [k]=OCV _(c1)(z _(c1) [k])+V _(impedance) _(_) _(c1) [k]V _(c2) [k]=OCV _(c2)(z _(c2) [k])+V _(impedance) _(_) _(c2) [k]V _(a) [k]=OCV _(a)(z _(a) [k])+V _(impedance) _(_) _(a) [k]

In the equations, k is a time index, which is a time parameter whichstarts from 0 and then increases by 1 whenever a preset time Δt passesif the voltage profile starts being estimated.

The z_(c1)[k] is a parameter which decreases from 1 to 0 in inverseproportion to the capacity ratio of already intercalated operating ionsinto the first cathode material in comparison to a gross capacity ofoperating ions capable of being intercalated into the first cathodematerial. Therefore, the z_(c1)[k] may be regarded as a parametercorresponding to the state (SOC) of the first cathode material.

The z_(c2)[k] is a parameter which decreases from 1 to 0 in inverseproportion to the capacity ratio of already intercalated operating ionsinto the second cathode material in comparison to a gross capacity ofoperating ions capable of being intercalated into the second cathodematerial. Therefore, the z_(c2)[k] may be regarded as a parametercorresponding to the state (SOC) of the second cathode material.

The z_(c1)[k] and z_(c2)[k] have a relationship with z_(cell)[k] whichis a state of the secondary battery, as follows.z _(cell) [k]=z _(c1) [k]Q* _(c1) +z _(c2) [k]Q* _(c2)

In this equation, Q*_(c1) represents a state ratio of the first cathodematerial, occupied in the state (SOC) of the secondary battery, whenz_(c1)[k] becomes 1, namely when operating ions are intercalated intothe first cathode material as much as possible. The Q*_(c1) correspondsto a value obtained by dividing the gross capacity (Ah) of operatingions capable of being intercalated into the first cathode material bythe gross capacity (Ah) of operating ions capable of being intercalatedinto the blended cathode material. Similarly, Q*_(c2) represents a stateratio of the second cathode material, occupied in the state (SOC) of thesecondary battery, when z_(c2)[k] becomes 1, namely when operating ionsare intercalated into the second cathode material as much as possible.The Q*_(c2) corresponds to a value obtained by dividing the grosscapacity (Ah) of operating ions capable of being intercalated into thesecond cathode material by the gross capacity (Ah) of operating ionscapable of being intercalated into the blended cathode material.

The Q*_(c1) and Q*_(c2) may vary within the range of 0 to 1 according toan operating voltage range of the secondary battery and may be easilycalculated through experiments.

The z_(a)[k] is a parameter which decreases from 1 to 0 in inverseproportion to the capacity ratio of operating ions alreadydeintercalated from the anode material in comparison to a gross capacityof operating ions capable of being deintercalated from the anodematerial. Therefore, the z_(a)[k] may be regarded as a parametercorresponding to the state (SOC) of the anode material and issubstantially identical to the state z_(cell)[k] of the secondarybattery.

The V_(c1)[k] is a voltage component formed by the first cathodematerial and includes two voltage components, namely an open-circuitvoltage component OCV_(c1)(z_(c1)[k]) varying according to z_(c1)[k] andan impedance voltage component V_(impedance) _(_) _(c1)[k] formed by theimpedance originating from an electrochemical characteristic of thefirst cathode material.

The V_(c2)[k] is a voltage component formed by the second cathodematerial and includes two voltage components, namely an open-circuitvoltage component OCV_(c2)(z_(c2)[k]) varying according to z_(c2)[k] andan impedance voltage component V_(impedance) _(_) _(c2)[k] formed by theimpedance originating from an electrochemical characteristic of thesecond cathode material.

The V_(a)[k] is a voltage component formed by the anode material andincludes two voltage components, namely an open-circuit voltagecomponent OCV_(a)(z_(a)[k]) varying according to z_(a)[k] and animpedance voltage component V_(impedance) _(_) _(a)[k] formed by theimpedance originating from an electrochemical characteristic of theanode material.

The i_(cell)[k] is a parameter representing current of the secondarybattery, which exhibits a discharge current when the secondary batteryis being discharged and has a value of 0 or near to 0 when the secondarybattery comes to an idle state or a no-load state.

The R₀ _(_) _(relax) is a parameter representing a resistance componentwhich disturbs the transfer of operating ions when voltage relaxationoccurs between the first and second cathode materials, and its valueincreases as more operating ions are intercalated into a cathodematerial (donor) which gives operating ions, when voltage relaxationstarts at the secondary battery, and decreases as a cathode material(receiver) which receives operating ions has a greater capacity whereoperating ions are capable of being intercalated. Therefore, assumingthat the first cathode material and the second cathode material arerespectively an operating ion receiver and a donor, the R₀ _(_) _(relax)may be expressed as a function defined by a relative ratio of thecapacity of operating ions already intercalated into the second cathodematerial in comparison to the capacity of operating ions capable ofbeing intercalated into the first cathode material. This assumption isapplied identically to the following disclosure. Since the R₀ _(_)_(relax) is a parameter which is considered when the secondary batterycomes to an idle state or a no-load state while being discharged in theintrinsic voltage range where the voltage relaxation occurs, if thevoltage relaxation does not occur, the R₀ _(_) _(relax) may not beconsidered as a parameter of the function f.

The function f may be obtained from a condition that a part of operatingions, deintercalated from the anode material and moving toward thecathode when the secondary battery is being discharged, is moved to thefirst cathode material and a remaining part of the operating ions moveto the second cathode material and a condition that the V_(c1)[k] andthe V_(c2)[k] are identical.

The function g may be obtained from a condition that a discharge currentof the secondary battery is proportional to a difference betweenV_(a)[k] and V_(anode)[k] when the secondary battery is being dischargedand is inversely proportional to the magnitude of impedance present atthe anode material.

According to the conditions above, a secondary battery including ablended cathode material may be equivalently analyzed as a circuitmodel, and the voltage estimating model may be derived from the circuitmodel.

The circuit model may include an anode material circuit unitcorresponding to the anode material and a cathode material circuit unitcorresponding to the blended cathode material and connected to the anodematerial circuit unit in series, and the cathode material circuit unitmay include a first cathode material circuit unit and a second cathodematerial circuit unit connected to each other in parallel.

According to the circuit model, the V_(impedance) _(_) _(c1)[k], theV_(impedance) _(_) _(c2)[k] and the V_(impedance) _(_) _(a)[k] arerespectively voltage components formed by impedance respectively presentat the first cathode material circuit unit, the second cathode materialcircuit unit and the anode material circuit unit.

The impedance may include a single circuit element or a plurality ofcircuit elements selected from the group consisting of one or moreresistance component, one or more capacity component, one or moreinductor component, and their combinations according to electrochemicalcharacteristics of the first and second cathode materials and the anodematerial. The impedance may include an RC circuit and/or a resistor, asan example. When the impedance includes the RC circuit and the resistor,the RC circuit and the resistor may be connected in series.

The V_(impedance) _(_) _(c1)[k], the V_(impedance) _(_) _(c2)[k] and theV_(impedance) _(_) _(a)[k] may be calculated from an impedance voltagecalculation equation which may be derived from a general circuit theory.Circuit elements included in the impedance may be connected in seriesand/or in parallel according to electrochemical properties of the firstand second cathode materials and the anode material. In the case an RCcircuit is included in the impedance, voltage formed by the RC circuitmay be regarded as varying according to time by a discrete time equationas follows.

${V\left\lbrack {k + 1} \right\rbrack} = {{{V\lbrack k\rbrack}e^{- \frac{\Delta\; t}{RC}}} + {{R\left( {1 - e^{- \frac{\Delta\; t}{RC}}} \right)}{i\lbrack k\rbrack}}}$

When analyzing electrochemical behaviors of the secondary battery wherethe voltage relaxation occurs by using the circuit model, the R₀ _(_)_(relax) may be considered as a serial resistance component presentbetween the first cathode material circuit unit and the second cathodematerial circuit unit. In this case, the R₀ _(_) _(relax) may beconsidered as a serial resistance component separately present betweenthe first cathode material circuit unit and the second cathode materialcircuit unit or a serial resistance component included in the impedancepresent at the first cathode material circuit unit and/or the secondcathode material circuit unit.

The OCV_(c1), OCV_(c1) and OCV_(a) are operators which convert statesz_(c1)[k], z_(c2)[k] and z_(a)[k] of the first cathode material, thesecond cathode material and the anode material into open-circuit voltagecomponents of the first cathode material, the second cathode materialand the anode material.

The operator may be a look-up table which allows reciprocal referencebetween the ‘state’ and the ‘open-circuit voltage’ or a look-up functionwhere a relationship between the ‘state’ and the ‘open-circuit voltage’is defined as a mathematical function.

The look-up table or the look-up function may be obtained by measuringan open-circuit voltage according to the change of state after making ahalf cell by using the first cathode material, the second cathodematerial and the anode material.

Regardless of the fact that the resistance component R₀ _(_) _(relax) isincluded in the circuit model, whenever k increases, the voltageestimating model updates z_(c1)[k], z_(c2)[k] and z_(a)[k] toz_(c1)[k+1], z_(c2)[k+1] and z_(a)[k+1], respectively, by theampere-counting method (see the equations below) during the time Δt,updates the V_(impedance) _(_) _(c1)[k], the V_(impedance) _(_) _(c2)[k]and the V_(impedance) _(_) _(a)[k] to V_(impedance) _(_) _(c1)[k+1], theV_(impedance) _(_) _(c2)[k+1] and the V_(impedance) _(_) _(a)[k+1],respectively, by using an impedance voltage calculation equation derivedfrom the circuit theory, and estimates V_(cell)[k+1] by calculatingV_(cathode)[k+1] and V_(anode)[k+1] by using the updated values.z _(c1) [k+1]=z _(c1) [k]+i _(c1) [k]Δt/Q _(c1)z _(c2) [k+1]=z _(c2) [k]+i _(c2) [k]Δt/Q _(c2)z _(a) [k+1]=z _(a) [k]−i _(a) [k]Δt/Q _(a) =z _(a) [k]−i _(cell)[k]Δt/Q _(a)

In the equations, i_(c1)[k] represents a current flowing through thefirst cathode material circuit unit while operating ions are beingintercalated into the first cathode material and may be calculated fromthe open-circuit voltage component OCV_(c1)(z_(c1)[k]) and the impedancevoltage component V_(impedance) _(_) _(c1)[k] of the first cathodematerial. Similarly, the i_(c2)[k] represents a current flowing throughthe second cathode material circuit unit while operating ions are beingintercalated into the second cathode material and may be calculated fromthe open-circuit voltage component OCV_(c2)(z_(c2)[k]) and the impedancevoltage component V_(impedance) _(_) _(c2)[k] of the second cathodematerial. In addition, the i_(a)[k] represents a current flowing throughthe anode material circuit unit as operating ions are deintercalatedfrom the anode material and is identical to the current i_(cell)[k] ofthe secondary battery, and the i_(cell)[k] may be measured whenever kincreases. In addition, Q_(c1) and Q_(c2) are respectively parametersrepresenting gross capacities (Ah) of the first cathode material and thesecond cathode material where operating ions may be intercalated, andQ_(a) is a parameter representing a gross capacity (Ah) of the anodematerial where operating ions may be deintercalated therefrom. Thei_(c1)[k] and the i_(c2)[k] have negative values when the secondarybattery is being discharged and have positive values when the secondarybattery is being charged. In addition, the i_(a)[k] and the i_(cell)[k]have positive values when the secondary battery is being discharged andhave negative values when the secondary battery is being charged.

The voltage profile estimated by the voltage estimating model exhibitsdifferent change patterns depending on the initial conditionsV_(impedance) _(_) _(c1)[0], V_(impedance) _(_) _(c2)[0], V_(impedance)_(_) _(a)[0], z_(c1)[0], z_(c2)[0] and z_(a)[0] as well as the magnitudeof R₀ _(_) _(relax) which is considered when voltage relaxation occursin the secondary battery.

However, since i_(cell)[0] has a value of 0 or near to 0 just after thesecondary battery comes to an idle state or a no-load state, the voltagecomponents V_(impedance) _(_) _(c1)[0], V_(impedance) _(_) _(c2)[0] andV_(impedance) _(_) _(a)[0] formed by the impedance present at the firstand second cathode materials circuit unit and the anode material circuitunit may be assumed to have a small value near to 0. In addition,z_(a)[0] substantially corresponds to z_(cell)[0] just after thesecondary battery comes to an idle state or a no-load state. Therefore,by regarding the voltage V_(cell)[0] measured just after the secondarybattery comes to an idle state or a no-load state as an open-circuitvoltage and using the look-up table or the look-up function where arelationship between the open-circuit voltage and the state of thesecondary battery is defined in advance through experiments, the stateof the secondary battery corresponding to the voltage V_(cell)[0] may beobtained and allocated to the initial condition z_(a)[0].

Therefore, the changing pattern of the voltage profile estimated by thevoltage estimating model may be regarded as being dependent on theinitial conditions z_(c1)[0] and z_(c2)[0] as well as the magnitude ofR₀ _(_) _(relax). In addition, since the magnitude of R₀ _(_) _(relax)has relations with the amount of operating ions intercalated into thefirst and second cathode materials just after the secondary batterycomes to an idle state or a no-load state as described above, it may beunderstood that the changing pattern of the voltage profile estimated bythe voltage estimating model will change mainly according to the initialconditions z_(c1)[0] and z_(c2)[0].

In an embodiment, if the occurrence of voltage relaxation is detectedfrom the voltage profile measured after the secondary battery comes toan idle state or a no-load state, the control unit may obtain aplurality of estimated profiles with respect to the voltage of thesecondary battery by repeatedly applying the voltage estimating model toeach combination (z_(c1)[0], z_(c2)[0], R₀ _(_) _(relax))_(p) whilevarying the values allocated to the initial conditions z_(c1)[0] andz_(c2)[0] and the value of R₀ _(_) _(relax) estimated therefrom. At thistime, the initial conditions V_(impedance) _(_) _(c1)[0], V_(impedance)_(_) _(c2)[0], V_(impedance) _(_) _(a)[0], and z_(a)[0] may be set underthe above conditions. Meanwhile, when changing the z_(c1)[0]_(p) andz_(c2)[0]_(p), it is possible to fix one and change the other or tochange both of them. When any one of the z_(c1)[0]_(p) and z_(c2)[0]_(p)is fixed, the fixed value is preferably set near a border value wherethe voltage relaxation starts occurring. The border value may be set asa value calculated in advance through experiments.

In addition, the control unit may identify an approximate estimatedprofile matched with the measured voltage profile, namely having asmallest error, from a plurality of estimated profiles, and estimate astate of the secondary battery by using the initial conditionsz*_(c1)[0] and z*_(c1)[0] which have been used for obtaining theapproximate estimated profile.z _(cell) =z* _(c1)[0]Q* _(c1) +z* _(c1)[0]Q* _(c2)

In another embodiment of the present disclosure, the control unit maycalculate a characteristic exhibited in the voltage profile when voltagerelaxation is detected as at least one reference parameter, and estimatea state of the secondary battery corresponding to the calculatedreference parameter with reference to the look-up table where arelationship between the reference parameter and the state of thesecondary battery are defined in advance through experiments.

The reference parameter may include any parameter if it may define ashape of the voltage profile having an inflection point. For example,the reference parameter includes a voltage at the inflection pointoccurring in the voltage profile, a time taken until the inflectionpoint occurs, a voltage variance amount obtained by adding voltagechanges before and after the inflection point, a slope of the voltageprofile (a first-order differential value) calculated at the inflectionpoint, a value obtained by integrating the voltage profile between aspecific point before the inflection point and a specific point afterthe inflection point, a first-order differential value or second-orderdifferential value of the voltage profile calculated at a specific pointbefore the inflection point and/or a specific point after the inflectionpoint, or their combinations. The reference parameter is an elementdefining the shape of the voltage profile having an inflection point.Therefore, the greater the number of reference parameters, the moreaccurate the shape of the voltage profile may be defined.

According to another aspect of the present disclosure, the relationshipbetween at least one reference parameter included in the look-up tableand the state of the secondary battery may be converted into a look-upfunction by numerical analysis. The look-up function means a functionwhich uses at least one reference parameter and a state of the secondarybattery corresponding thereto as an input parameter and an outputparameter, respectively.

In this case, the control unit may calculate a characteristic exhibitedin the voltage profile when voltage relaxation is detected as at leastone reference parameter, and estimate a state of the secondary batterycorresponding to the calculated reference parameter by putting thereference parameter as an input parameter to the look-up function wherethe relationship between the reference parameter and the state of thesecondary battery is defined in advance.

According to another embodiment of the present disclosure, the controlunit may analyze the voltage measured by the sensor in real time, andthen, if the calculated inflection point parameter corresponds to acondition under which voltage relaxation is detected, the control unitmay estimate a state of the secondary battery by using the calculatedinflection point parameter at that time, a voltage measured when thecondition under which voltage relaxation is detected is established, atime when the voltage is measured, or the like.

For example, whenever a voltage is measured by the sensor, the controlunit may receive the voltage value from the sensor and calculate afirst-order differential value or a second-order differential value ofthe voltage value with respect to the measurement time as an inflectionpoint parameter, and then, if a condition under which the first-orderdifferential value becomes maximum or the second-order differentialvalue becomes zero is established, the control unit may determine themaximum value of the first-order differential value and/or the timetaken until the condition is established and/or a voltage when thecondition is established as a reference parameter and estimate a stateof the secondary battery by using the determined reference parameter.

Here, the inflection point parameter represents a parameter by which aninflection point may be identified in real time in the changing patternof a voltage, and the above descriptions are just examples. Therefore,any parameter by which an inflection point occurring in the changingpattern of the voltage measured by the sensor 120 may be identified inreal time may be determined as the inflection point parameter.

According to another aspect of the present disclosure, the control unitmay update the state of the secondary battery, estimated before thesecondary battery comes to an idle state or a no-load state, to thestate of the secondary battery, estimated by the above method.

According to another aspect of the present disclosure, the control unitmay be electrically connected to a display unit and display the state ofthe secondary battery estimated at an idle state or a no-load state as agraphic interface through the display unit.

The graphic interface is an interface visually displaying the state ofthe secondary battery, and its kind is not specially limited. Thegraphic interface may adopt displaying the state of the secondarybattery with the length of a bar graph, displaying the state of thesecondary battery with gauge pointers, displaying the state of thesecondary battery with numerals, or the like, without being limitedthereto.

According to another aspect of the present disclosure, the control unitmay be electrically connected to a storage unit and may maintain thevoltage data and/or the current data provided by the sensor and theestimated state of the secondary battery in the storage unit.

Here, the maintaining work means storing and updating data in thestorage unit. The control unit may output the state of the secondarybattery, which is maintained in the storage unit, as a graphic interfacethrough the display unit.

The present disclosure may also provide a method for managing asecondary battery including a cathode having a first cathode materialand a second cathode material, which includes different operatingvoltage ranges, an anode, and a separator.

The secondary battery managing method includes obtaining a current and avoltage of the secondary battery during operation of the secondarybattery over a predetermined amount of time; preparing a voltage profileand optionally a current profile from the measured current and voltageof the secondary battery; detecting a voltage relaxation duringoperation of the secondary battery, said voltage relaxation beinginduced by the transfer of operating ions between the first and secondcathode active materials when the secondary battery comes to an idlestate or a no-load state; and if a voltage relaxation is detected,estimating a state of charge (SOC) using the voltage profiles of thesecondary battery.

The present disclosure may also provide a method for manufacturing thesecondary battery described above. The secondary battery manufacturingmethod may include at least a process of preparing the blended cathodematerial where at least first and second cathode materials are blended.The first and second cathode materials are selected to have differentoperating voltage ranges and allow voltage relaxation by transferringthe operating ions between the first and second cathode materials whenthe secondary battery comes to an idle state or a no-load state in anintrinsic voltage range.

The kind and blending ratio of the first and second cathode materialsmay be determined according to the kind of the secondary battery, andavailable commercial cathode materials may be used without restriction.In addition, in order to improve electrochemical characteristics of theblended cathode material, cathode materials other than the first andsecond cathode materials may be added to the blended cathode materialwithout restriction.

The secondary battery manufacturing method may further include a processof forming slurry containing the blended cathode material and otheradditives, for example a conducting agent, a binder and an organicsolvent.

The secondary battery manufacturing method may further include a processof forming a cathode material coating layer on a metallic currentcollector by coating at least one surface of the metallic currentcollector with the slurry and then drying and compressing the same.

The secondary battery manufacturing method may further include a processof forming an anode and a process of packaging the secondary battery.

The secondary battery manufacturing method may further include a processof activating (formation) the secondary battery to be capable of beingcharged or discharged in a voltage range including the intrinsic voltagerange.

Meanwhile, the technical spirit of the present disclosure may besimilarly applied to a case in which the cathode has a single cathodematerial and the anode has two or more anode materials.

In this case, the voltage relaxation may occur when a secondary batterycomes to an idle state or a no-load state while being charged. Here, theno-load state means a state in which a charge current is 0, and the idlestate is defined above.

In an embodiment, the anode of the secondary battery may include firstand second anode materials having different operating voltage ranges,and the first anode material may be activated at a lower voltage range(or, at a low level of SOC) than the second anode material. In otherwords, if the secondary battery has a low voltage, operating ions may bemainly intercalated into the first anode material, while if thesecondary battery has a high voltage, operating ions may be mainlyintercalated into the second anode material.

In this case, if the SOC of a secondary battery in a charge mode startsincreasing from 0%, operating ions are mainly intercalated into thefirst anode material. In addition, if the SOC of the secondary batteryincreases until the capacity of the first anode material to whichoperating ions may be intercalated is mostly used, the resistance of thefirst anode material rapidly increases, and operating ions start beingintercalated into the second anode material. Moreover, if the secondarybattery comes to an idle state or a no-load state after operating ionsare intercalated into the second anode material to some extent, apotential difference is created between the first anode material and thesecond anode material, which may cause a voltage relaxation in which theoperating ions intercalated into the second anode material aretransferred to the first anode material.

Generally, if the charging process stops, the voltage of the secondarybattery represent a decreasing pattern while converging toward theopen-circuit voltage. However, if a voltage relaxation occurs, thevoltage of the secondary battery converges toward the open-circuitvoltage while exhibiting a voltage decreasing pattern including aninflection point.

Therefore, if a voltage profile of a secondary battery is measured whenthe secondary battery comes to an idle state or a no-load state whilebeing charged, a voltage relaxation may be detected from the measuredvoltage profile, and optionally a state of the secondary battery may beestimated from the voltage profile by using a voltage estimating modelderived from the circuit model.

In order to detect the occurrence of a voltage relaxation, variousmethods described above may be applied. In addition, the circuit modeldescribed above may be easily changed by those skilled in the art byconsidering that blended anode materials are included in the anode ofthe secondary battery and a single cathode material is included in thecathode of the secondary battery. In other words, the circuit model usedfor deriving the voltage estimating model may be replaced with a circuitmodel including an anode material circuit unit having a first anodematerial circuit unit and a second anode material circuit unit and acathode material circuit unit, and the current flowing on each circuitunit and the voltage formed at a circuit element included in eachcircuit unit may be reinterpreted in light of charging the secondarybattery including the blended anode materials, as obvious to thoseskilled in the art.

In addition, the technical spirit of the present disclosure may also besimilarly applied to a case in which blended cathode materials andblended anode materials are respectively included in the cathode and theanode of the secondary battery.

In this case, a voltage relaxation may occur in both the discharge modeand the charge mode. In other words, the voltage relaxation may occurwhen a secondary battery in the discharge mode comes to an idle state ora no-load state in a voltage range in which a voltage relaxation mayoccur or when a secondary battery in the charge mode comes to an idlestate or a no-load state in a voltage range in which a voltagerelaxation may occur.

The voltage relaxation occurring in the discharge mode or the chargemode may be detected by measuring a voltage profile of the secondarybattery. In addition, optionally, a state of the secondary battery maybe estimated from the measured voltage profile by using the voltageestimating model according to the present disclosure.

The circuit model used for deriving the voltage estimating model may bereplaced with a circuit model including an anode material circuit unithaving a first anode material circuit unit and a second anode materialcircuit unit and a cathode material circuit unit having a first cathodematerial circuit unit and a second cathode material circuit unit, andthe current flowing on each circuit unit and the voltage formed at acircuit element included in each circuit unit may be reinterpreted inlight of charging or discharging the secondary battery including theblended cathode materials and the blended anode materials.

Advantageous Effects

According to an aspect of the present disclosure, it is possible toquantitatively and qualitatively understand a voltage relaxationphenomenon which is a specific voltage behavior when mixing cathodematerials with different operating voltage ranges. Therefore, it ispossible to commercially use a blended cathode material in a voltagerange where charge/discharge control is not easily implemented due to adistinct voltage behavior caused by the voltage relaxation phenomenon.

According to another aspect of the present disclosure, it is possible toestimate a state of a secondary battery in an intrinsic voltage rangewhere a distinct voltage behavior occurs due to the voltage relaxation.Therefore, cathode materials, which were not capable of blending due tothe distinct voltage behavior, may be blended into various combinations.In addition, by selecting two or more cathode materials among variouskinds of available cathode materials and blending them into variouscombinations according to the purpose of a secondary battery, it ispossible to provide a blended cathode material most appropriatelyoptimized for the purpose of the secondary battery.

According to another aspect of the present disclosure, the distinctvoltage behavior becomes a factor which does not allow variousadjustment of a blending ratio of the blended cathode material. However,since the distinct voltage behavior may be accurately interpreted, amixture ratio of cathode materials included in the blended cathodematerial may be adjusted in various ways according to the purpose of thesecondary battery.

According to another aspect of the present disclosure, it is possible toaccurately estimate a state of the secondary battery in the intrinsicvoltage range exhibiting the distinct voltage behavior.

According to another aspect of the present disclosure, when a secondarybattery comes to an idle state or a no-load state, the state of thesecondary battery may be updated by using the state of the secondarybattery estimated in the intrinsic voltage range. Therefore, an erroraccumulated while estimating a state of the secondary battery may beeliminated.

According to another aspect of the present disclosure, since variouscathode materials may be blended with various compositions and atvarious ratios according to the purpose of a secondary battery, it ispossible to dynamically deal with the diversification of cathodematerial or requirements of the technical fields to be recently in thelimelight such as electric vehicles or power storage devices.

According to another aspect of the present disclosure, by providing notonly the blended cathode material but also a secondary battery havingthe same, a method for manufacturing the same, and a method andapparatus for estimating a state of a secondary battery having theblended cathode material, it is possible to give a total solutionrequired for commercially using the blended cathode material.

DESCRIPTION OF DRAWINGS

The accompanying drawing illustrates a preferred embodiment of thepresent disclosure and together with the foregoing disclosure, serves toprovide further understanding of the technical spirit of the presentdisclosure. However, the present disclosure is not construed as beinglimited to the drawing.

FIG. 1 is a diagram for illustrating a voltage relaxation phenomenonoccurring in a secondary battery having a blended cathode material;

FIG. 2 is a graph showing a voltage change pattern of a secondarybattery when the secondary battery comes to a no-load state in anintrinsic voltage range where voltage relaxation occurs;

FIG. 3 is a graph showing that the voltage change pattern of thesecondary battery exhibited due to the occurrence of voltage relaxationchanges according to a state of the secondary battery;

FIG. 4 is a graph showing that the voltage change pattern of thesecondary battery exhibited due to the occurrence of voltage relaxationchanges according to a discharge condition of the secondary battery;

FIG. 5 is a graph showing dQ/dV distribution of a lithium secondarybattery having an NMC cathode material and an LFP cathode material;

FIG. 6 is a graph showing a discharge resistance profile of a lithiumsecondary battery having an NMC cathode material and an LFP cathodematerial;

FIG. 7 is a graph showing a discharge profile of a lithium secondarybattery having an NMC cathode material and an LFP cathode material;

FIG. 8 is a graph showing measurement results of voltage profilesaccording to states of a half cell manufactured so that an NMC cathodematerial and a lithium metal are respectively used as a cathode and ananode and a half cell manufactured so that an LFP cathode material and alithium metal are respectively used as a cathode and an anode;

FIG. 9 is a diagram exemplarily showing parameters useable foridentifying the occurrence of voltage relaxation;

FIG. 10 is a block diagram showing an apparatus for managing a secondarybattery according to an embodiment of the present disclosure;

FIG. 11 is a circuit diagram showing a circuit model according to anembodiment of the present disclosure;

FIG. 12 is a graph showing a voltage profile of a secondary battery,estimated using a voltage estimating model according to an embodiment ofthe present disclosure;

FIGS. 13 to 15 are circuit diagrams exemplarily showing variousconnection manners of a resistance component (R₀ _(_) _(relax)) which isa factor disturbing the transfer of operating ions when the voltagerelaxation occurs in the secondary battery;

FIG. 16 is a graph showing that a voltage profile estimated by thevoltage estimating model may be closely matched with an actual voltageprofile when the resistance component (R₀ _(_) _(relax)) is reflected tothe circuit model;

FIG. 17 is a graph showing that a voltage profile matched with variousvoltage change patterns may be estimated by changing the magnitude of R₀_(_) _(relax) even though the voltage change pattern exhibited due tothe occurrence of voltage relaxation varies according to a state or adischarge condition of the secondary battery;

FIG. 18 is a graph showing that the magnitude of the resistancecomponent (R₀ _(_) _(relax)) may be estimated by using a parameter(X_(relax)) defined by states (z_(c1), z_(c2)) of first and secondcathode materials;

FIGS. 19 and 20 are flowcharts for illustrating a method for managing asecondary battery according to an embodiment of the present disclosure;

FIG. 21 is a flowchart for illustrating a method for estimating a stateof a secondary battery by means of iteration;

FIG. 22 is a graph showing that the state of a secondary batteryestimated according to an embodiment of the present disclosure isclosely matched with an actual state of the secondary battery;

FIG. 23 is a graph showing that initial conditions for states of thefirst and second cathode materials are important parameters greatlyinfluencing the magnitude of the resistance component (R₀ _(_) _(relax))when the state of the secondary battery is estimated according to anembodiment of the present disclosure; and

FIG. 24 is a diagram showing various examples of a useable graphicinterface to display the state of a secondary battery, estimatedaccording to an embodiment of the present disclosure.

BEST MODE

Hereinafter, preferred embodiments of the present disclosure will bedescribed in detail with reference to the accompanying drawings. Priorto the description, it should be understood that the terms used in thespecification and the appended claims should not be construed as limitedto general and dictionary meanings, but interpreted based on themeanings and concepts corresponding to technical aspects of the presentdisclosure on the basis of the principle that the inventor is allowed todefine terms appropriately for the best explanation. Therefore, thedescription proposed herein is just a preferable example for the purposeof illustrations only, not intended to limit the scope of thedisclosure, so it should be understood that other equivalents andmodifications could be made thereto without departing from the spiritand scope of the disclosure.

The embodiments described below are based on cases where the presentdisclosure is applied to a lithium secondary battery. Here, the lithiumsecondary battery is a general name of a secondary battery where lithiumions serve as operating ions during charge and discharge to causeelectrochemical reactions at a cathode and an anode. The operating ionsmean ions participating in electrochemical oxidizing and reducingreactions while the secondary battery is charged or discharged, and maybe for example lithium. Therefore, even though secondary batteries arecalled differently according to the kind of electrolyte or separatorused in the lithium secondary battery, the kind of package used forpacking the secondary battery, or the internal or external structure ofthe lithium secondary battery, such secondary batteries should beinterpreted as being included in the scope of the lithium secondarybattery if lithium ions are used as operating ions.

In addition, the present disclosure may also be applied to kinds ofsecondary batteries other than the lithium secondary batteries.Therefore, all kinds of secondary batteries should be interpreted asbeing included in the scope of the present disclosure if the spirit ofthe present disclosure may be applied even though their operating ion isnot a lithium ion. In some embodiments, the term “secondary battery” isused instead of “lithium secondary battery” and in this case, it shouldbe understood that the term has a meaning including various kinds ofsecondary batteries in the corresponding embodiment.

Moreover, the secondary battery is not limited to the number of itscomponents. Therefore, the secondary battery should be interpreted asincluding a unit cell having an anode, an electrolyte and a cathode as abasic unit, an assembly of unit cells, a module having a plurality ofassemblies connected in series in/or in parallel, a pack having aplurality of modules connected in series in/or in parallel, a batterysystem having a plurality of packs connected in series in/or inparallel, or the like.

FIG. 1 is a diagram for illustrating a voltage relaxation phenomenonoccurring in a blended cathode material according to the presentdisclosure. In detail, FIG. 1 depicts that a voltage relaxation occursbetween cathode materials when a secondary battery including a blendedcathode material, where two cathode materials having different degreesof reaction with lithium ions serving as operating ions of a lithiumsecondary battery (namely, having different operating voltage ranges)are blended, is discharged in an intrinsic voltage range and comes to ano-load state while being discharged.

As shown in FIG. 1, while the lithium secondary battery is discharged,lithium ions electrochemically react with a first cathode material 10and a second cathode material 20. The electrochemical reaction meansthat the lithium ions are intercalated into the first and second cathodematerials 10, 20 or deintercalated therefrom. Since the electrochemicalreaction may be varied according to an operating mechanism of thelithium secondary battery, the present disclosure is not limited to areaction type of operating ions.

The first and second cathode materials 10, 20 have different reactionconcentrations of lithium ions reacting therewith according to thechange of voltage. In other words, the first and second cathodematerials 10, 20 have different operating voltage ranges. For example,under the condition where the secondary battery is discharged, in acertain voltage range, lithium ions may be preferentially intercalatedinto the first cathode material 10 rather than the second cathodematerial 20, and at another voltage range, it may be the opposite. Asanother example, under the condition where the lithium secondary batteryis charged, in a certain voltage range, operating ions may bepreferentially de-intercalated from the second cathode material 20rather than the first cathode material 10, and at another voltage range,it may be the opposite.

FIG. 1 shows an example where the concentration of lithium ions reactingwith the first cathode material 10 is greater than the concentration oflithium ions reacting with the second cathode material 20 when thelithium secondary battery is discharged. If the voltage of the lithiumsecondary battery varies, the reaction concentrations of lithium ionsreacting with the first and second cathode materials 10, 20 may bereversed.

The lithium ions intercalated into the first and second cathodematerials 10, 20 diffuse into the cathode materials, and in this processa lithium ion concentration deviation occurs near and in the surface ofthe cathode materials. The black solid lines represent the change oflithium concentration inside the cathode materials or near theirsurfaces, and it may be understood that the concentration of lithiumions is greater near the surface than the inside of the first and secondcathode materials 10, 20 in both cases, and the concentration of lithiumions gets smaller from the vicinity of the surface to the inside.

The voltage of the secondary battery measured when the lithium secondarybattery is discharged is generally determined by the concentration oflithium ions present near the surface of the cathode material. Inaddition, in view of electric potential, when the lithium secondarybattery is in a discharge mode, surface potentials V₁, V₂ of the firstand second cathode materials 10, 20 have no significant difference. Inthe art, the voltage measured when a lithium secondary battery isdischarged is called a dynamic voltage.

Meanwhile, if the lithium secondary battery comes to a no-load state,the reaction of the first and second cathode materials 10, 20 withlithium ions stops, and lithium ions are diffused in the first andsecond cathode materials 10, 20 due to the deviation of lithium ionconcentration. Therefore, if the no-load state is maintained for apredetermined time, the voltage of the lithium secondary battery isdetermined according to the average concentration of lithium ionspresent in the first and second cathode materials 10, 20. Further, inview point of electric potential, the potential V_(OCV1) of the firstcathode material 10 marked by a dotted line becomes higher than thepotential V_(OCV2) of the second cathode material 20 marked by a dottedline, and the difference between the potentials V_(OCV1) and V_(OCV2)increases as the no-load state is maintained longer. Hereinafter, thevoltage measured when the secondary battery comes to a no-load state iscalled a no-load voltage.

In the present disclosure, the no-load state means a state where thesecondary battery stops charging or discharging and so the capacity ofthe secondary battery is substantially not changing or the change isnegligible. If the change of the capacity of the secondary battery isnegligible when the secondary battery is in an idle state, the idlestate may also be regarded as being substantially equivalent to theno-load state.

As described above, if the potentials V_(OCV1) and V_(OCV2) of the firstand second cathode materials 10, 20 are different in the condition thatthe lithium secondary battery is in the no-load state, a potentialdifference is generated between the first and second cathode materials10, 20, and if the potential difference increases so much to cause thetransfer of lithium ions, lithium ions start to move from the secondcathode material 20 to the first cathode material 10. If lithium ionsmove between the cathode materials, the potential of the second cathodematerial 20 giving lithium ions increases, and the potential of thefirst cathode material 10 receiving lithium ions decreases. The secondcathode material 20 is charged (the potential increases) as lithium ionsescape, and the first cathode material 10 is discharged (the potentialdecreases) as lithium ions are intercalated. If lithium ions movebetween the first and second cathode materials 10, 20 as describedabove, the potential difference between the first and second cathodematerials 10, 20 slowly decreases, and at an equilibrium state wherelithium ions no longer move further, the first and second cathodematerials 10, 20 have identical potential.

In the present disclosure, the concept ‘voltage relaxation’ may bedefined by peculiar electrochemical behaviors of the blended cathodematerial as described above. In other words, the ‘voltage relaxation’may be defined as a following phenomenon: when a lithium secondarybattery in a discharge mode comes to an idle state or a no-load state,lithium ions are diffused in the first and second cathode materials 10,20 included in the blended cathode material, the diffused lithium ionscause a potential difference between the first and second cathodematerials 10, 20, and the potential difference causes transfer oflithium ions between the cathode materials, thereby slowly decreasingthe potential difference.

However, the voltage relaxation phenomenon is generated in a partialvoltage range, not in the entire voltage range where a lithium secondarybattery having the blended cathode material is discharged. In otherwords, when the lithium secondary battery comes to an idle state or ano-load state while being discharged in the partial voltage range, thevoltage relaxation phenomenon is generated. The partial voltage rangemay be changed according to various factors such as the kind or blendingratio of the first and second cathode materials 10, 20, an magnitude ofa discharge current, a state (SOC) of the secondary when the secondarybattery comes to the idle state or the no-load state, but in view of theblended cathode material, the partial voltage range corresponds to aninherent voltage range of each blended cathode material. Therefore, thepartial voltage range where the voltage relaxation phenomenon occurswill be called an ‘intrinsic voltage range’.

If the lithium secondary battery is discharged in the intrinsic voltagerange, among the first and second cathode materials 10, 20, the firstcathode material 10 easily reacting with lithium ions is almostcompletely reacted with lithium ions. Therefore, in view of lithiumions, it is difficult to react with the first cathode material 10. Inother words, if a dynamic voltage is within the intrinsic voltage rangewhile the lithium secondary battery is being discharged, the resistanceof the first cathode material 10 rapidly increases, and as a result theresistance of the second cathode material 20 relatively decreases incomparison to the first cathode material 10. Therefore, lithium ionsreact with the second cathode material 20 having relatively lowresistance and start to be intercalated into the second cathode material20. If this situation is maintained for a predetermined time and thenthe lithium secondary battery comes to an idle state or a no-load statewhen the concentration of lithium ions mainly present near the surfaceof the second cathode material 20 increases to some extent, the voltagerelaxation phenomenon described above occurs. In other words, thevoltage relaxation phenomenon may be regarded as occurring if thelithium secondary battery comes to the idle state or the no-load stateat an early stage where most of the capacity of the first cathodematerial 10 for intercalation of lithium ions is exhausted and thesecond cathode material 20 starts reacting with lithium ions.

FIG. 2 is a graph showing the pattern of no-load voltage changingaccording to time when a lithium secondary battery including a blendedcathode material where a lithium transition metal oxideLi_(1+x)Ni_(a)Co_(b)Mn_(c)O₂ (x≥0; a=b=c=⅓; hereinafter, referred to asan NMC cathode material) having a layered structure as the first cathodematerial and LiFePO₄ (referred to as an LFP cathode material) having anolivine structure as the second cathode material are blended at a ratioof 7:3 (weight ratio) comes to a no-load state while being dischargedfrom 3.2V (SOC 32%) belonging to the intrinsic voltage range near to 3V.

Referring to FIG. 2, the changing pattern of the no-load voltage of thelithium secondary battery may be divided into first to third regions (I,II and III) in general for consideration.

In the first region (I), a dynamic voltage of a lithium secondarybattery having a voltage of 3.2V (SOC 32%) slowly decreases while thelithium secondary battery is being discharged near to 3V. If the lithiumsecondary battery has a dynamic voltage of 3.2V, the capacity of thefirst cathode material does not have much room for intercalation oflithium ions. Therefore, if the lithium secondary battery is dischargedfrom 3.2V to 3.0V, the lithium ions mostly react with the second cathodematerial rather than with the first cathode material, and so theconcentration of lithium ions near the surface of the second cathodematerial increases.

In the second region (II), the lithium secondary battery comes to ano-load state while discharging stops near 3.0V, and the no-load voltageof the lithium secondary battery slowly increases as lithium ions arediffused in the first and second cathode materials of the blendedcathode material.

Meanwhile, at a border of the first region (I) and the second region(II), the no-load voltage of the lithium secondary battery rapidlyincreases because an IR drop voltage substantially becomes 0 (zero) asthe lithium secondary battery stops discharging. In other words, if thelithium secondary battery stops discharging, a voltage drop caused bythe IR drop phenomenon disappears, and the no-load voltage of thelithium secondary battery increases as much as the IR voltage drop.

In the third region (III), as lithium ions are diffused in the first andsecond cathode materials, a potential difference is generated betweenthe cathode materials, operating ions are transferred between thecathode materials due to the generated potential difference to cause avoltage relaxation phenomenon, and as the voltage relaxation of thecathode materials progresses, the no-load voltage of the lithiumsecondary battery slowly increases near to 3.5V corresponding to anequilibrium voltage. Here, the equilibrium voltage means a voltage atwhich the no-load voltage of the lithium secondary battery does notsubstantially change.

Meanwhile, the second region (II) and the third region (III) arerepresented to partially overlap each other since operating ions causingvoltage relaxation between the cathode materials start transferringbefore lithium ions are ‘completely’ diffused in the cathode materials(namely, before the second region ends) and so a border between thesecond region (II) and the third region (III) may not be clearlydistinguished.

In FIG. 2, it should be noted that an inflection point (marked with adotted circle) is present between the second region (II) and the thirdregion (III). This supports that a dominating electrochemical mechanismcausing the increase of a no-load voltage changes before or after theappearance of the inflection point, while the no-load voltage of thelithium secondary battery increases to 3.5V corresponding to theequilibrium voltage after the lithium secondary battery stopsdischarging. Here, the term ‘dominating’ means that a certainelectrochemical mechanism is superior to other electrochemicalmechanism. In other words, it may be regarded that the no-load voltageof the lithium secondary battery generally increases due to thediffusion of lithium ions in the cathode materials before the inflectionpoint appears, and the no-load voltage of the lithium secondary batterygenerally increases due to voltage relaxation of the cathode materialscaused by the transfer of operating ions between the cathode materialsafter the inflection point appears.

The voltage changing pattern shown in FIG. 2 shows two-stage voltagerises. A first-stage voltage rise occurs before an inflection pointappears, and a second-stage voltage rise occurs after the inflectionpoint appears. Therefore, voltage relaxation of a secondary batteryincluding a blended cathode material in a cathode, which exhibits thevoltage changing pattern as shown in FIG. 2, may be called two-stagevoltage relaxation.

FIG. 3 is a graph showing the change of no-load voltage of the lithiumsecondary battery under each SOC condition when discharging is stoppedafter performing 9C pulse discharge within a short time while changing astate z_(cell) of the lithium secondary battery having a blended cathodematerial where an NMC cathode material and an LFP cathode material areblended at a ratio of 7:3 (weight ratio) variously to 0.90, 0.80, 0.40,0.30, 0.20 and 0.10. In FIG. 3, z_(cell) represents a state of thelithium secondary battery. In addition, at each voltage profile, adotted line represents a dynamic voltage measured in a pulse dischargeregion, and a solid line represents a no-load voltage measured in theno-load state region.

Referring to FIG. 3, it may be understood that the inflection pointsupporting the occurrence of voltage relaxation starts appearing when astate of the lithium secondary battery decreases to about 0.40, and thevoltage relaxation is maintained until the state becomes about 0.20. Inother words, the voltage relaxation phenomenon appears when a state ofthe lithium secondary battery is within the range of 0.2 to 0.4 (markedwith a rectangle).

The state of the lithium secondary battery is proportional to thedynamic voltage of the lithium secondary battery. In other words, if thedynamic voltage increases, the state increases, and if the dynamicvoltage decreases, the state also decreases. Therefore, the intrinsicvoltage range where the voltage relaxation phenomenon appears may beconverted into a state range of the lithium secondary battery. For thisreason, even though the intrinsic voltage range is converted into astate range of a secondary battery, the state range may be regarded asbeing substantially equivalent to the intrinsic voltage range, andtherefore the state range of 0.2 to 0.4 should be understood as anotherkind of numerical expression of the intrinsic voltage range. Therefore,the state range of 0.2 to 0.4 may be regarded as an inherent state rangecorresponding to the intrinsic voltage range.

Meanwhile, it may be understood that, as the state of the lithiumsecondary battery is nearer to 0.20, the time taken until the occurrenceof the inflection point or the time for the voltage of the lithiumsecondary battery to reach an equilibrium voltage increases. It isestimated that this increase of time is caused by the following reasons.In other words, as the state of the lithium secondary battery becomesnearer to 0.20, the NMC cathode material mostly reacts with lithium ionsand so the resistance of the NMC cathode material further increases. Inaddition, the amount of lithium ions intercalated into the LFP cathodematerial also further increases. Therefore, in order to transfer thelithium ions intercalated into the LFP cathode material toward the NMCcathode material by means of the voltage relaxation phenomenon, moretime is required in proportion to the increase of resistance of the NMCcathode material and the increased amount of lithium ions intercalatedinto the LFP cathode material.

FIG. 4 is a graph showing results of an experiment which evaluates aninfluence of the magnitude of a discharge current on the voltagerelaxation phenomenon.

The voltage profiles of FIG. 4 show the change of no-load voltage of thelithium secondary battery according to time, when the lithium secondarybattery having the same blended cathode material as in the formerembodiment stops pulse discharge while being pulse-discharged for 10seconds at various states (0.190˜0.333) and various discharge currents(2 c, 5 c, 9 c) which allow the voltage relaxation phenomenon. Here, ‘c’represents c-rate of the discharge current.

In FIG. 4, left, central and right graphs show voltage profiles whenpulse discharge is stopped while being performed at 2 c, 5 c and 9 c,respectively.

Referring to FIG. 4, if the discharge current is identical, the lowerthe state of a secondary battery is, the later an inflection pointsupporting the occurrence of voltage relaxation appears. If theoccurrence of the inflection point is delayed, the point of time whenthe no-load voltage of the lithium secondary battery reaches anequilibrium state is also delayed.

In addition, when the state of the secondary battery is identical, thehigher the discharge current is, the later the inflection point appearsin the voltage profile. If comparing three voltage profiles obtainedwhen the state is 0.262, the voltage rapidly changes when the magnitudeof the discharge current is 2 c, and so the inflection point appearsjust after the pulse discharge stops and the voltage reaches anequilibrium state within a short time. Meanwhile, it may also beunderstood that, when the magnitude of the discharge current is 5 c and9 c, the voltage changes gradually and the inflection point appearslate, and so the time taken until the occurrence of the inflection pointis longer in the case where the magnitude of the discharge current is 9c, in comparison to the case where the magnitude of the dischargecurrent is 5 c. From these facts, the following may be deduced, and eachdeduction conforms to the consideration results of the voltage profilesshown in FIG. 4.

First, when the discharge current is identical, the lower the state ofthe secondary battery is, the greater the amount of lithium ionsreacting with the LFP cathode material (a reaction concentration) is.The low state means that the resistance of the NMC cathode materialincreases that much more and so the possibility that lithium ionssupplied by the discharge current reacts with the LFP cathode materialincreases. The increased amount of lithium ions reacting with the LFPcathode material also increases the time taken for transferring thelithium ions during the voltage relaxation. The increased time may bechecked from the phenomenon that the occurrence of the inflection pointand the time taken for the no-load voltage of the lithium secondarybattery to reach an equilibrium state are delayed as the state of thesecondary battery is lower in the voltage profiles of FIG. 4.

In addition, under the condition that the state of the secondary batteryis identical, if the discharge current increases, the concentration oflithium ions reacting with the NMC cathode material increases, and theresistance of the NMC cathode material increases that much faster.Therefore, if the discharge current increases under the condition thatthe state of the secondary battery is identical, the time when lithiumions start reacting with the LFP cathode material is advanced and so anamount of lithium ions intercalated into the LFP cathode materialfurther increases. Therefore, if the voltage relaxation phenomenonoccurs, the time for the lithium ions intercalated in the LFP cathodematerial to be transferred to the NMC cathode material increases inproportion to the amount of lithium ions reacting with the LFP. Theincreased time may be checked from the fact that the occurrence of theinflection point and the time taken for the no-load voltage of thelithium secondary battery to reach an equilibrium state are delayed inthe voltage profiles.

In addition, if considering the above two deductions together, it mayalso be deduced that the state of a secondary battery where voltagerelaxation starts is lowered as the discharge current is lower. In otherwords, if the discharge current is lowered in the intrinsic voltagerange where voltage relaxation occurs, the increase of resistance of theNMC cathode material moderates, and so the possibility that lithium ionsadditionally react with the NMC cathode material increases. Therefore,lithium ions still react with the NMC cathode material even in acondition that voltage relaxation starts when the discharge current islarge. Therefore, under the condition that discharge current is low, thereaction between lithium ions and the LFP cathode material may beinitiated only when the state is further lowered.

Next, conditions required for the blended cathode material having thefirst and second cathode materials to cause voltage relaxation in theintrinsic voltage range will be described in detail.

In an embodiment, the voltage relaxation may occur when, at themeasurement of dQ/dV distribution of the first and second cathodematerials, the cathode materials are different from each other inlocations of their main peaks and/or intensities of the main peaksexhibited in the dQ/dV distribution.

Here, the dQ/dV distribution, as known in the art, represents a capacitycharacteristic of the cathode material at various operating voltages.The difference in locations of the main peaks may be changed dependingon the kinds of the first and second cathode materials. For example, thedifference in locations of the main peaks may be 0.1 to 4V.

FIG. 5 is a graph showing measurement results of dQ/dV distribution,obtained by applying 1 c-rate discharge condition to a lithium secondarybattery having a blended cathode material where an NMC cathode materialand an LFP cathode material are blended at a ratio of 7:3 (weightratio).

Referring to FIG. 5, two main peaks are present in the dQ/dVdistribution, where the left peak corresponds to a main peak of the LFPcathode material and the right peak corresponds to a main peak of theNMC cathode material. In addition, profiles around the main peak of theLFP cathode material are generated as lithium ions react with the LFPcathode material, and profiles around the main peak of the NMC cathodematerial are generated as lithium ions react with the NMC cathodematerial. The dQ/dV distribution shown in FIG. 5 supports the fact thatthe NMC cathode material and the LFP cathode material have differentoperating voltage ranges.

As shown in FIG. 5, it may be understood that the difference oflocations of the main peaks shown in the dQ/dV distribution of the NMCcathode material and the LFP cathode material is about 0.4V, and theintensity of the main peak of the LFP cathode material is about twotimes greater than that of the NMC cathode material. The NMC cathodematerial and the LFP cathode material having such dQ/dV characteristicexhibits a voltage relaxation phenomenon in the intrinsic voltage range,as described above with reference to FIG. 2. Therefore, if locations ofthe main peaks and/or intensities of the main peaks exhibited in thedQ/dV distribution of the first and second cathode materials used forblending are different, namely if the first and second cathode materialshave different operating voltage ranges, the blended cathode materialwhere the first and second cathode materials are blended may be regardedas satisfying the condition of causing a voltage relaxation phenomenonin the intrinsic voltage range regardless of the kind of the first andsecond cathode materials.

In another embodiment, when measuring a discharge resistance of thelithium secondary battery containing the blended cathode material atvarious SOCs, the voltage relaxation may occur when the dischargeresistance profile has a convex pattern or when the discharge resistanceprofile has two inflection points before and after the top of the convexpattern.

FIG. 6 is a discharge resistance profile showing measurement results ofa discharge resistance according to the change of SOC with respect to alithium secondary battery including the blended cathode material wherean NMC cathode material and an LFP cathode material are blended at aratio of 7:3 (weight ratio).

Referring to FIG. 6, it may be understood that the discharge resistanceprofile of the lithium secondary battery including the blended cathodematerial has a convex pattern when SOC is about 20 to 40%. In addition,it may also be understood that two inflection points (marked by a dottedcircle) occurs when SOC is in the range of 20 to 30% and in the range of30 to 40%, respectively, in the discharge resistance profile. Inaddition, it may be understood that the discharge resistance of thelithium secondary battery rapidly increases when SOC belongs to therange of 30 to 40%, and this may originate from the fact that theresistance of the NMC cathode material rapidly increases as most of thecapacity of the NMC cathode material to which lithium ions may beintercalated is exhausted. The lithium secondary battery including theblended cathode material where the NMC cathode material and the LFPcathode material are blended exhibits a voltage relaxation phenomenon inthe intrinsic voltage range as described above with reference to FIG. 2.Therefore, when the discharge resistance profile of the lithiumsecondary battery has a convex pattern or when the discharge resistanceprofile has two inflection points before and after the top of the convexpattern, the blended cathode material where the first and second cathodematerials are blended may be regarded as satisfying the conditioncausing a voltage relaxation phenomenon in the intrinsic voltage rangeregardless of the kinds of the first and second cathode materials.

As another embodiment, the voltage relaxation may occur when the lithiumsecondary battery having the blended cathode material has a charge ordischarge profile with at least one voltage plateau.

FIG. 7 is a discharge profile showing measurement results of anopen-circuit voltage at various SOCs, obtained while discharging alithium secondary battery including the blended cathode material wherean NMC cathode material and an LFP cathode material are blended at aratio of 7:3 (weight ratio).

Referring to FIG. 7, it may be understood that the discharge profile ofthe lithium secondary battery including the blended cathode material hasa voltage plateau looking as if there is substantially no voltagechange, namely as if the voltage is substantially constant, based on thenaked eye, when the open-circuit voltage is about 3.2V. The voltageplateau may be checked identically when measuring an open-circuitvoltage at various SOCs while charging the lithium secondary batteryincluding the blended cathode material where an NMC cathode material andan LFP cathode material are blended at a ratio of 7:3 (weight ratio).The lithium secondary battery including the blended cathode materialwhere an NMC cathode material and an LFP cathode material are blendedexhibits a voltage relaxation phenomenon in the intrinsic voltage range,as described above with reference to FIG. 2. From this, it may beconfirmed that, when the charge or discharge profile of the lithiumsecondary battery has at least one voltage plateau, the blended cathodematerial where the first and second cathode materials are blendedsatisfies the condition of causing a voltage relaxation phenomenon inthe intrinsic voltage range regardless of the kinds or blending ratio ofthe first and second cathode materials.

FIG. 8 is a graph showing measurement results of voltage profiles at astate range of 0-1 with respect to a half cell manufactured so that anNMC cathode material and a lithium metal are respectively used as acathode and an anode and a half cell manufactured so that an LFP cathodematerial and a lithium metal are respectively used as a cathode and ananode.

In FIG. 8, graph {circle around (1)} depicts a voltage profile of thehalf cell including the NMC cathode material and graph {circle around(2)} depicts a voltage profile of the half cell including the LFPcathode material.

Referring to FIG. 8, a voltage plateau is observed in the voltageprofile including the LFP cathode material.

This measurement results supports that in a secondary battery using ablended cathode material including an NMC cathode material and a LFPcathode material, at an early stage where the state z starts decreasingfrom 100%, the NMC cathode material is activated so that lithium ionsare mainly intercalated to the NMC cathode material; if the state zdecreases so that the voltage of the secondary battery is lowered to thelevel of the intrinsic voltage range, the LFP cathode material isactivated so that lithium ions start being intercalated into the LFPcathode material; and if the state z of the secondary battery comes to0%, the states z of the NMC cathode material and the LFP cathodematerial also become 0%, which means that the capacity of each cathodematerial capable of accommodating a lithium ion is entirely used.

In an aspect, the graph of FIG. 8 supports that when at least one of thefirst and second cathode materials included in the blended cathodematerial has a voltage profile with a voltage plateau under the halfcell condition, the secondary battery including the blended cathodematerial exhibits a voltage relaxation in the intrinsic voltage range.

In another aspect, the graph of FIG. 8 supports that when one of thefirst and second cathode materials included in the blended cathodematerial has a voltage profile with a voltage plateau under the halfcell condition and the other has a voltage profile without a voltageplateau and with a higher voltage in comparison to the voltage profilewith a voltage plateau in at least a part of the entire state under thehalf cell condition, the secondary battery including the blended cathodematerial exhibits a voltage relaxation in the intrinsic voltage range.

In the present disclosure, the first and second cathode materials mayuse any material without limitation if it may cause voltage relaxationin the intrinsic voltage range. Therefore, any combination of cathodematerials satisfying at least one of the above conditions may beconsidered as the first and second cathode materials, in addition to theNMC cathode material and the LFP cathode material, as obvious to thoseskilled in the art.

In an embodiment, the first cathode material may be an alkali metalcompound expressed by a general chemical formula A[A_(x)M_(y)]O_(2+z),wherein A includes at least one of Li, Na and K; M includes at least oneelement selected from the group consisting of Ni, Co, Mn, Ca, Mg, Al,Ti, Si, Fe, Mo, V, Zr, Zn, Cu, Al, Mo, Sc, Zr, Ru and Cr; x≥0, 1≤x+y≤2,−0.1≤z≤2; and x, y, z and stoichiometric coefficients of the componentsincluded in M are selected so that the alkali metal compound maintainselectrical neutrality.

Alternatively, the first cathode material may be an alkali metalcompound expressed by xLiM¹O₂-(1−x)Li₂M²O₃ wherein M¹ includes at leastone element with an average oxidation state of +3; M² includes at leastone element with an average oxidation state of +4; and 0≤x≤1, andselectively coated with a carbon layer, an oxide layer and a fluoridelayer, which is disclosed in U.S. Pat. Nos. 6,677,082, 6,680,143 or thelike.

In another embodiment, the second cathode material may be lithium metalphosphate expressed by a general chemical formula Li_(a)M¹_(x)Fe_(1−x)M² _(y)P_(1−y)M³ _(z)O_(4−z), wherein M¹ includes at leastone element selected from the group consisting of Ti, Si, Mn, Co, V, Cr,Mo, Fe, Ni, Nd, Al, Mg and Al; M² includes at least one element selectedfrom the group consisting of As, Sb, Si, Ge, V and S; M³ includes atleast one element selected from a halogen group containing F; 0<a≤2,0≤x≤1, 0≤y<1, 0≤z<1; and a, x, y, z, and stoichiometric coefficients ofthe components included in M¹ _(x), M² _(y), and M³ _(z) are selected sothat the lithium metal phosphate maintains electrical neutrality, orLi₃M₂(PO₄)₃ wherein M includes at least one element selected from thegroup consisting of Ti, Si, Mn, Co, V, Cr, Mo, Ni, Al, Mg and Al.

In another embodiment, the first cathode material may be an alkali metalcompound expressed by Li[Li_(a)Ni_(b)Co_(c)Mn_(d)]O_(2+z) (a≥0;a+b+c+d=1; at least one of b, c and d is not zero; −0.1≤z≤2). The secondcathode material may be at least one selected from the group consistingof LiFePO₄, LiMn_(x)Fe_(y)PO₄ (0<x+y≤1) and Li₃Fe₂(PO₄)₃.

In another embodiment, the first cathode material and/or the secondcathode material may include a coating layer. The coating layer mayinclude a carbon layer, or an oxide layer or a fluoride layer containingat least one selected from the group consisting of Ti, Si, Mn, Co, V,Cr, Mo, Fe, Ni, Nd, Al, Mg, Al, As, Sb, Si, Ge, V and S.

In the present disclosure, the kind and blending ratio of the first andsecond cathode materials may be suitably selected or adjusted inconsideration of the use of a secondary battery to be manufactured, anelectrochemical design condition for the secondary battery, anelectrochemical characteristic of cathode materials required for causinga voltage relaxation between the cathode materials, an intrinsic voltagerange where voltage relaxation occurs, or the like.

In an embodiment, if a secondary battery with a good discharge power isdesired, a cathode material having a good reactivity with lithium ionsmay be selected as one of the first and second cathode materials, and amixture ratio of the corresponding cathode material may be set as highas possible under the condition causing a voltage relaxation (satisfyingat least one of the above conditions). For example,Li[Ni_(1/3)Mn_(1/3)Co_(1/3)]O₂ and LiFePO₄ may be respectively selectedas the first cathode material and the second cathode material, and amixture ratio of the first cathode material and the second cathodematerial may be set to be 5:5.

In another embodiment, if a secondary battery with high-temperaturestability is desired, a cathode material with excellent high-temperaturestability may be selected as one of the first and second cathodematerials, and a mixture ratio of the corresponding cathode material maybe set as high as possible under the condition causing a voltagerelaxation (satisfying at least one of the above conditions). Forexample, Li[Ni_(1/3)Mn_(1/3)Co_(1/3)]O₂ and LiFePO₄ may be respectivelyselected as the first cathode material and the second cathode material,and a mixture ratio of the first cathode material and the second cathodematerial may be set to be 2:8.

In another embodiment, if a secondary battery with a low production costis desired, a cathode material with a low production cost may beselected as one of the first and second cathode materials, and a mixtureratio of the corresponding cathode material may be set as high aspossible under the condition causing a voltage relaxation (satisfying atleast one of the above conditions). For example,Li[Ni_(1/3)Mn_(1/3)Co_(1/3)]O₂ and LiFePO₄ may be respectively selectedas the first cathode material and the second cathode material, and amixture ratio of the first cathode material and the second cathodematerial may be set to be 1:9.

In another embodiment, if a secondary battery having a good dischargepower and excellent high-temperature stability is desired, a cathodematerial having a good reactivity with operating ions and a cathodematerial having excellent high-temperature stability may be respectivelyselected as the first and second cathode materials, and a mixture ratioof the cathode materials may be set in consideration of balancing of thedischarge power and the high-temperature stability under the conditioncausing a voltage relaxation (satisfying at least one of the aboveconditions). For example, Li[Ni_(1/3)Mn_(1/3)Co_(1/3)]O₂ and LiFePO₄ maybe respectively selected as the first cathode material and the secondcathode material, and a mixture ratio of the first cathode material andthe second cathode material may be set to be 4:6.

In another embodiment, if a secondary battery having a great capacityper weight is desired, a cathode material having a great capacity perweight may be selected as one of the first and second cathode materials,and a mixture ratio of the corresponding cathode material may be set tobe as high as possible under the condition causing a voltage relaxation(satisfying at least one of the above conditions). For example,Li[Ni_(0.5)Mn_(0.3)Co_(0.2)]O₂ and LiFePO₄ may be respectively selectedas the first cathode material and the second cathode material, and amixture ratio of the first cathode material and the second cathodematerial may be set to be 9:1.

The selection of the first and second cathode materials and theadjustment of their mixture ratio described above are just examples.Therefore, it is obvious to those skilled in the art that the first andsecond cathode materials may be suitably selected and a mixture ratio ofthe cathode materials may be suitably set in consideration of relativeweights and balances of electrochemical properties to be endowed to theblended cathode material under the condition of causing voltagerelaxation in an intrinsic voltage range.

In addition, the number of kinds of cathode materials included in theblended cathode material is not limited to two. In addition, forenhancing properties of the blended cathode material, other additivessuch as a conducting agent, a binder or the like may be added to theblended cathode material without special limitation. Therefore, if ablended cathode material includes at least two cathode materials capableof causing voltage relaxation when the secondary battery comes to anidle state or a no-load state in the intrinsic voltage range, thisshould be understood as belonging to the scope of the present disclosureregardless of the number of cathode materials and the presence of otheradditives, as obvious to those skilled in the art.

In the present disclosure, the blended cathode material including atleast the first and second cathode materials may be used as a cathodematerial of a secondary battery which is charged or discharged in avoltage range including the intrinsic voltage range in order to utilizethe voltage relaxation phenomenon.

The secondary battery may be loaded on various kinds of electric-drivenapparatuses which operate with electric energy, and the kind of theelectric-driven apparatus is not specially limited.

In an embodiment, the electric-driven apparatus may be a mobile computerdevice such as a cellular phone, a laptop, and a tablet computer; or ahand-held multimedia device such as a digital camera, a video camera,and an audio/video regenerating device.

In another embodiment, the electric-driven apparatus may be anelectric-powered apparatus such as an electric vehicle, a hybridvehicle, an electric bike, a motor cycle, an electric train, an electricship, and an electric airplane; or a motor-mounted power tool such as anelectric drill and an electric grinder.

In another embodiment, the electric-driven apparatus may be a largepower storage device installed at a power grid to store new regenerationenergy or surplus energy, or an uninterrupted power supply for supplyingpower to various information communication devices such as servercomputers and mobile communication devices in times of emergency such asa blackout.

The blended cathode material described above may be included in acathode of a secondary battery. The secondary battery may furtherinclude an anode and a separator in addition to the cathode. Inaddition, the secondary battery may be charged or discharged in avoltage range including the intrinsic voltage range where the blendedcathode material causes voltage relaxation.

In an embodiment, the cathode may include a thin-plate metallic currentcollector made of conductive material, and a cathode material coatinglayer containing the blended cathode material and formed on at least onesurface of the metallic current collector.

The metallic current collector is made of material with chemicalstability and high conductivity. For example, the metallic currentcollector may be made of aluminum, stainless steel, nickel, titanium,sintered carbon or the like. As another example, the metallic currentcollector may be made of aluminum or stainless steel coated with carbon,nickel, titanium, silver or the like on the surface thereof.

The cathode material coating layer may further include additives such asa conducting agent and a binder in addition to the blended cathodematerial.

The conducting agent is not specially limited if it may improve electricconductivity of the blended cathode material, and may use variousconductive carbonaceous materials such as graphite, carbon black,acetylene black, Ketjen black, Super-P, carbon nano tube or the like,without being limited thereto.

The binder is not specially limited if it allows a close physical jointamong particles of the blended cathode material and a close interfacialjoint between the blended cathode material and the metallic currentcollector. Various kinds of polymers such as poly(vinylidenefluoride-co-hexafluoropropylene polymer) (PVDF-co-HFP), polyvinylidenefluoride, polyacrylonitrile, polymethyl methacrylate or the like may beused as the binder, without being limited thereto.

In an embodiment, the anode may include a thin-plate metallic currentcollector made of conductive material, and an anode material coatinglayer containing anode material and formed on at least one surface ofthe metallic current collector.

The metallic current collector is made of material with chemicalstability and high conductivity. For example, the metallic currentcollector may be made of copper, aluminum, stainless steel, nickel,titanium, sintered carbon or the like. As another example, the metalliccurrent collector may be made of copper or stainless steel coated withcarbon, nickel, titanium, silver or the like on the surface thereof oran aluminum-cadmium alloy.

The anode material is not specially limited if it has a differentoxidation/reduction potential (redox potential) from the blended cathodematerial and allows intercalation of operating ions during the chargingprocess and deintercalation of operating ions during the dischargingprocess.

The anode material may use carbonaceous material, lithium metal,silicon, tin or the like, without being limited thereto, and may alsouse metal oxides such as TiO₂ and SnO₂ with a potential lower than 2V.Preferably, the anode material may use carbonaceous material, and thecarbonaceous material may use both low crystalline carbon and highcrystalline carbon. The low crystalline carbon representatively includessoft carbon and hard carbon, and the high crystalline carbonrepresentatively includes high-temperature sintered carbon such asnatural graphite, Kish graphite, pyrolytic carbon, mesophase pitch basedcarbon fiber, meso-carbon microbeads, mesophase pitches, petroleumderived cokes, and tar pitch derived cokes.

The anode material coating layer may further include additives such as aconducting agent and a binder in addition to the anode material. Theconducting agent and the binder may use materials which are available asa conducting agent and a binder included in a cathode material coatinglayer.

The separator is not specially limited if it has a pore structure forelectrically separating the cathode and the anode and allowing thetransfer of operating ions.

In an embodiment, the separator may use a porous polymer film, forexample a porous polymer film made from polyolefin-based polymer such asethylene homopolymer, propylene homopolymer, ethylene/butene copolymer,ethylene/hexene copolymer, and ethylene/methacrylate copolymer, or theirlaminates. As other examples, a common porous non-woven fabric madefrom, for example, high-melting glass fibers or polyethyleneterephthalate fibers may be used.

Meanwhile, at least one surface of the separator may include a coatinglayer of inorganic particles. In addition, the separator may be made ofa coating layer of inorganic particles. The particles of the coatinglayer may have a structure coupled with a binder so that interstitialvolumes are present among adjacent particles. This structure isdisclosed in PCT International Publication WO 2006/025662, which may beincorporated herein by reference. The inorganic particles may be made ofinorganic material with a dielectric constant of 5 or above. Theinorganic materials may include at least one selected from the groupconsisting of Pb(Zr,Ti)O₃ (PZT), Pb_(1−x)La_(x)Zr_(1−y)Ti_(y)O₃ (PLZT),PB (Mg₃Nb_(2/3))O₃—PbTiO₃ (PMN-PT), BaTiO₃, hafnia (HfO₂), SrTiO₃, TiO₂,Al₂O₃, ZrO₂, SnO₂, CeO₂, MgO, CaO, ZnO and Y₂O₃, without being limitedthereto.

The secondary battery may also further include an electrolyte containingoperating ions. The electrolyte is not specially limited if it mayinclude operating ions and cause an electrochemical oxidation orreduction reaction at the cathode and the anode by means of theoperating ions.

The electrolyte may be a salt having a structure of A⁺B⁻, without beinglimited thereto. Here, the A⁺ includes alkali metallic cations such asLi⁺, Na⁺, and K⁺ or their combinations. In addition, B⁻ includes atleast one anion selected from the group consisting of F⁻, Cl⁻, Br⁻, I⁻,NO₃ ⁻, N(CN)₂ ⁻, BF₄ ⁻, ClO₄ ⁻, AlO₄ ⁻, AlCl₄ ⁻, PF₆ ⁻, SbF₆ ⁻, AsF₆ ⁻,BF₂C₂O₄ ⁻, BC₄O₈ ⁻, (CF₃)₂PF₄ ⁻, (CF₃)₃PF₃ ⁻, (CF₃)₄PF₂ ⁻, (CF₃)₅PF⁻,(CF₃)₆P⁻, CF₃SO₃ ⁻, C₄F₉SO₃ ⁻, CF₃CF₂SO₃ ⁻, (CF₃SO₂)₂N⁻, (FSO₂)₂N⁻,CF₃CF₂(CF₃)₂CO⁻, (CF₃SO₂)₂CH⁻, (SF₅)₃C⁻, (CF₃SO₂)₃C⁻, CF₃(CF₂)₇SO₃ ⁻,CF₃CO₂ ⁻, CH₃CO₂ ⁻, SCN⁻, and (CF₃CF₂SO₂)₂N⁻.

The electrolyte may also be used in a state of being dissolved in anorganic solvent. The organic solvent may use propylene carbonate (PC),ethylene carbonate (EC), diethyl carbonate (DEC), dimethyl carbonate(DMC), dipropyl carbonate (DPC), dimethyl sulfoxide, acetonitrile,dimethoxyethane, diethoxyethane, tetrahydrofuran, N-methyl-2-pyrrolidone(NMP), ethyl methyl carbonate (EMC), γ-butyrolactone, or their mixtures.

In an embodiment, the secondary battery may further include a packagefor sealing the cathode, the anode and the separator. In the case thecathode, the anode and the separator are sealed by the package, thecathode and the anode may be respectively jointed to a cathode terminaland an anode terminal, and the cathode terminal and the anode terminalmay be led out of the package. On occasions, in the case the packageserves as an electrode terminal, either the cathode terminal or theanode terminal may be replaced with the package. For example, if theanode is electrically connected to the inside of the package, the outersurface of the package may function as an anode. The package is notspecially limited if it has chemical stability and may be made of metal,polymer, a flexible pouch film or the like, without being limitedthereto. The flexible pouch film may be representatively an aluminumpouch film where a thermal bonding layer, an aluminum layer and an outerprotection layer are laminated.

The appearance of the secondary battery is determined by the structureof the package. The package may adopt any structure used in the art andits appearance according to the use of a battery is not speciallylimited. The package may have structures such as a cylindrical shape, arectangular shape, a pouch shape, a coin shape, or curved shapes thereofwithout being limited thereto.

In another embodiment of the present disclosure, the blended cathodematerial may be preferably used in a cathode forming process, which isincluded in the secondary battery manufacturing method.

In an embodiment, the secondary battery manufacturing method may includea process of preparing a blended cathode material where at least thefirst and second cathode materials described above are blended.

The first and second cathode materials are selected to have differentconcentrations of operating ions reacting therewith according to thechange of voltage and allow voltage relaxation by transferring theoperating ions between the first and second cathode materials whencoming to an idle state or a no-load state in the intrinsic voltagerange.

The kinds and mixture ratios of the first and second cathode materialsmay be determined according to the kind of the secondary battery, andcommercially available cathode materials may be used without limitation.In addition, in order to improve the electrochemical characteristic ofthe blended cathode material, it is not ruled out to add a cathodematerial other than the first and second cathode materials to theblended cathode material.

The secondary battery manufacturing method may further include a processof forming slurry including the blended cathode material and otheradditives such as a conducting agent, a binder and an organic solvent.Here, the conducting agent, the binder and the organic solvent may besuitably selected from the materials disclosed above so that thecharacteristic of the blended cathode material is desirably exhibited.

The secondary battery manufacturing method may further include a processof forming a cathode material coating layer on the metallic currentcollector by coating the metallic current collector with the slurry onat least one surface thereof, and then drying and compressing the same.

The secondary battery manufacturing method may further include a processof forming an anode and a process of packaging a secondary battery.These additional processes may be selected from various techniques knownin the art in consideration of the kind and structure of the secondarybattery so that the blended cathode material may manifest the optimalperformance. Therefore, the additional processes described below arejust examples, not limiting the scope of the present disclosure.

In an embodiment, the secondary battery manufacturing method may furtherinclude a process of forming an anode. The anode may be formed bycoating at least one surface of the metallic current collector withslurry including anode material and other additives, for example aconducting agent, a binder and an organic solvent and then drying andcompressing the same. The anode material, the conducting agent, thebinder and the organic solvent may be suitably selected from thematerials disclosed above so that the characteristic of the blendedcathode material is manifested desirably.

The secondary battery manufacturing method may further include a processof forming an electrode assembly by interposing a separator between thecathode and the anode.

The electrode assembly includes a unit cell having at least a laminatedstructure of cathode/separator/anode. The unit cell may have variousstructures known in the art. For example, the unit cell may have abi-cell structure where outermost electrodes have the same polarity or afull-cell structure where outermost electrodes have opposite polarities.The bi-cell may have a structure ofcathode/separator/anode/separator/cathode, for example. The may have astructure of, for example,cathode/separator/anode/separator/cathode/separator/anode.

The electrode assembly may have various structures known in the art, andfor example the electrode assembly may have a simple stack structurewhere the unit cell and an insulating film are repeatedly laminated fromthe bottom to the top. In addition, the electrode assembly may have astack folding structure formed by disposing unit cells on a insulativefolding film at regular intervals and then rolling the insulativefolding film together with the unit cells in a predetermined direction.In addition, the electrode assembly may have a jelly roll structureformed by placing a unit cell prepared in a sheet shape extending in onedirection on a insulative rolling film and then rolling the unit celland the insulative rolling film together.

The secondary battery manufacturing method may further include a processof forming a secondary battery by sealing the electrode assembly in apackage together with an electrolyte. The electrolyte may be suitablyselected from the materials disclosed above so that the characteristicof the blended cathode material is manifested desirably. In addition,the electrolyte is not specially limited in its physical phase and somay be used as a solid electrolyte, a liquid electrolyte, a gelelectrolyte or the like. The electrolyte may be injected into thepackage as a separate process when the electrode assembly is loaded inthe package or may be immersed in the electrode assembly in advance. Inthe case the solid electrolyte may be used as the separator, theseparator may be replaced with a solid electrolyte film.

The secondary battery manufacturing method may further include a processof activating (forming) the secondary battery to be capable of beingcharged or discharged in a voltage range including the intrinsic voltagerange. The activating process includes a step of performing an initialcharge so that the secondary battery may be used in a voltage rangeincluding the intrinsic voltage range. The intrinsic voltage range ischanged depending on the kind of the blended cathode material. Forexample, in the case the first and second cathode materials are an NMCcathode material and an LFP cathode material, the intrinsic voltagerange includes a range of 2.5 to 4.3V. The activating process may alsoselectively include a step of discharging gas collected in the package,when the initial charging step is performed.

The secondary battery manufacturing method may further include a processof welding a metallic electrode lead to a tab, if the tab is drawn outof the metallic current collector included in the cathode and the anode.If this process is included, the process of sealing an electrode currentcollector in the package is preferably performed so that one end of theelectrode lead is exposed out.

In another embodiment of the present disclosure, the secondary batteryincluding the blended cathode material may be electrically connected orcoupled to a control unit which monitors an electric characteristiccaused from the voltage relaxation when coming to an idle state or ano-load state.

Here, the electric connection means that the control unit iselectrically coupled to a cathode and an anode of the secondary batteryso that an electric characteristic such as voltage and current of thesecondary battery may be measured.

The control unit may selectively include processors well known in theart, ASIC (application-specific integrated circuit), other chipsets,logic circuits, registers, communication modems, data processing devicesor the like in order to execute various control logics described below.In addition, when the control logic is implemented as software, thecontrol unit may be implemented as an aggregate of program modules. Atthis time, program modules are stored in a memory and executed byprocessors. The memory unit may be present in or out of the processorand may be connected to the processor by various means. In addition, thememory may be included in a storage unit (see FIG. 10) of the presentdisclosure. Moreover, the memory is a general name to call devicesstoring information, regardless of the kind of devices, without beinglimited to a specific memory device.

The control unit may be a battery management system (BMS) which may beelectrically coupled to a secondary battery, or a control elementincluded in the BMS.

The BMS may be interpreted as meaning a typical BMS system in the art,but in the functional point of view, any system capable of performing atleast one function disclosed in this specification may be included inthe scope of the BMS.

The control unit may monitor a voltage characteristic of the secondarybattery and detect that a voltage relaxation phenomenon occurs betweenthe first and second cathode materials included in the secondarybattery. Here, the voltage characteristic is an example and may bevoltages of the secondary battery repeatedly measured at time intervalsafter the secondary battery comes to an idle state or a no-load state.The voltages may configure a voltage profile exhibiting the change ofvoltages according to time when being considered together with themeasurement time.

The control unit may indirectly detect that voltage relaxation occurs inthe blended cathode material included in the secondary battery byanalyzing the voltage profile.

FIG. 9 is a graph showing an example of the voltage profile exhibitedwhen voltage relaxation occurs, which shows various factors useable forthe control unit to detect the occurrence of voltage relaxation.

As shown in FIG. 9, if voltage relaxation occurs, an inflection point Cis generated between the time point when the secondary battery comes toan idle state or a no-load state and the time point when the voltage ofthe secondary battery reaches an equilibrium state. Therefore, whetherthe inflection point C occurs, and/or whether the time τ_(relax) takenuntil the occurrence of the inflection point C belongs to a criticaltime range, and/or whether the voltage profile slope at the inflectionpoint C belongs to a critical slope range may be considered as factors.

In addition, if the secondary battery stops discharging, a voltage dropeffect caused by IR drop disappears. Therefore, just after dischargingis stopped, the voltage rapidly increases as much as the IR dropvoltage. After that, a first voltage rise ΔV₁ occurs before aninflection point is generated in the voltage profile, and a secondvoltage rise ΔV₂ occurs after the inflection point is generated.Therefore, whether two voltage rises occur before and after theinflection point, and/or whether a voltage variance amount ΔV_(relax)obtained by adding the first and second voltage rises belongs to thecritical voltage range, or whether the time taken until the occurrenceof the voltage rise ΔV₁ and/or ΔV₂ belongs to the critical time rangemay be considered as factors.

Here, the critical voltage range, the critical slope range, and thecritical time range may be determined in advance through experiments,and may be inherently set according to the kind and blending ratio ofcathode materials included in the blended cathode material.

According to the present disclosure, the control unit may detect theoccurrence of voltage relaxation in the blended cathode materialincluded in the secondary battery by monitoring a voltage characteristicof the secondary battery in consideration of various identifying factorsdescribed above, after the secondary battery comes to an idle state or ano-load state.

In an embodiment, the control unit may monitor a voltage variance amountof the secondary battery during a preset measurement time and checkwhether the voltage variance amount belongs to the critical voltagerange, after the secondary battery comes to an idle state or a no-loadstate while being discharged.

Here, the critical voltage range and the measurement time may be set inadvance through experiments. In other words, the critical voltage rangeand the measurement time may be set by discharging a secondary batteryincluding the blended cathode material in an intrinsic voltage rangewhere voltage relaxation may occur and then stopping discharge so thatthe secondary battery comes to an idle state or a no-load state, andthen analyzing a voltage profile of the secondary battery exhibited atthis time. During the experiment procedure, voltage, magnitude ofdischarge current, SOC or the like when coming to an idle state or ano-load state are variously changed under the condition where voltagerelaxation may Occur.

The critical voltage range and the measurement time may be changeddepending on the blended cathode material included in the secondarybattery and may be set in consideration of a plurality of data relatingto the voltage variance amount obtained from a plurality of voltageprofiles and a plurality of time data taken for detecting the voltagevariance amount.

For example, the critical voltage range and the measurement time may berespectively set in the range of 50 to 400 mV and 5 to 100 seconds,without being limited thereto.

In the above embodiment, if a voltage variance amount belonging to thecritical voltage range is monitored during the measurement time, thecontrol unit may indirectly detect the occurrence of voltage relaxationin the blended cathode material included in the secondary battery, andoptionally quantitatively estimate a state of the secondary batterycorresponding to the voltage change of the secondary battery monitoredduring the measurement time. A method for quantitatively estimating astate of the secondary battery will be described later in detail.

In another embodiment, the control unit may monitor whether aninflection point C is generated in a voltage profile measured during apreset measurement time after the secondary battery comes to an idlestate or a no-load state while being discharged, and/or whether a slopeof the voltage profile calculated at the inflection point C belongs to acritical slope range, and/or whether the time τ_(relax) taken until theoccurrence of the inflection point C belongs to a critical time range.

Here, the measurement time may be set through experiments similar to theabove description. In other words, the measurement time may be set bydischarging a secondary battery including the blended cathode materialin the intrinsic voltage range where voltage relaxation may occur andstopping the discharge so that the secondary battery comes to an idlestate or a no-load state, and then analyzing the time taken until theoccurrence of the inflection point C in the voltage profile of thesecondary battery. In the experiment procedure, voltage, magnitude ofdischarge current, SOC or the like when the secondary battery coming toan idle state or a no-load state are variously changed under thecondition where voltage relaxation may occur.

In this embodiment, if the occurrence of the inflection point Csupporting the occurrence of voltage relaxation in the voltage profile,and/or a voltage profile slope at the inflection point C belonging tothe critical slope range, and/or the time of occurrence of inflectionpoint C belonging to the critical time range are checked, the controlunit may indirectly detect the occurrence of voltage relaxation in theblended cathode material included in the secondary battery, andoptionally quantitatively estimate a state of the secondary batterycorresponding to the voltage change of the secondary battery, monitoredduring the measurement time.

In another embodiment, the control unit may monitor whether two voltagerises ΔV₁, ΔV₂ are detected before and after the inflection point Csupporting the occurrence of voltage relaxation in the voltage profilemeasured for a preset measurement time after the secondary battery comesto an idle state or a no-load state while being discharged, and/orwhether a voltage variance amount ΔV_(relax) obtained by adding twovoltage rises belongs to the critical voltage range, and/or and whetherthe time taken during the voltage variations of ΔV₁ and/or ΔV₂ belongsto the critical time range.

Here, the measurement time may be set through experiments similar to theabove description. In other words, the measurement time may be set bydischarging a secondary battery including the blended cathode materialin the intrinsic voltage range where voltage relaxation may occur andstopping the discharge so that the secondary battery comes to an idlestate or a no-load state, and then analyzing a time interval of twodetected voltage rises before and after the inflection point Csupporting the occurrence of voltage relaxation in the voltage profileof the secondary battery, and/or the time taken for detecting thevoltage variance amount ΔV_(relax) and/or and the time taken during thevoltage variations of ΔV₁ and/or ΔV₂. In the experiment procedure,voltage, magnitude of discharge current, SOC or the like when thesecondary battery coming to an idle state or a no-load state arevariously changed under the condition where voltage relaxation mayoccur.

In this embodiment, if two voltage rises ΔV₁, ΔV₂ before and after theinflection point C supporting the occurrence of voltage relaxation inthe voltage profile, and/or the voltage variance amount ΔV_(relax)belonging to the critical voltage range, and/or the rises of voltagesΔV₁ and/or ΔV₂ under the time condition belonging to the critical timerange are detected, the control unit may indirectly detect theoccurrence of voltage relaxation in the blended cathode materialincluded in the secondary battery, and optionally quantitativelyestimate a state of the secondary battery corresponding to the voltagechange of the secondary battery, monitored during the measurement time.

In another embodiment of the present disclosure, a secondary batteryincluding the blended cathode material having at least the first andsecond cathode materials and exhibiting a voltage relaxation phenomenonin the intrinsic voltage range may be coupled with a secondary batterymanaging apparatus which estimates a state of the secondary battery.

FIG. 10 is a block diagram schematically showing a secondary batterymanaging apparatus 100 according to an embodiment of the presentdisclosure.

As shown in FIG. 10, the secondary battery managing apparatus 100includes a sensor 120 for measuring an electric characteristic of thesecondary battery 110 for a predetermined measurement time when thesecondary battery 110 comes to an idle state or a no-load state whilebeing discharged, and a control unit 130 for detecting the occurrence ofthe voltage relaxation based on the measured electric characteristic andoptionally estimating a state of the secondary battery 110 correspondingto the voltage relaxation.

Here, the measurement time may be set in different ways depending on themethod for the control unit 130 to identify the voltage relaxation. Themeasurement time setting method may use any one of methods disclosedabove in the former embodiments.

The electric characteristic is an example and may include a voltagebetween the cathode and the anode of the secondary battery 110 and acurrent of the secondary battery 110.

The electric characteristic may be repeatedly measured at regularintervals during the measurement time. In this case, data relating torepeatedly measured electric characteristic may form a profile.

For example, if the voltage of secondary battery 110 is measured severaltimes for the measurement time as the electric characteristic, themeasured voltage data may form a voltage profile. As another example, ifthe current of the secondary battery 110 is measured several times forthe measurement time as the electric characteristic, the measuredcurrent data may form a current profile.

The control unit 130 receives a measurement value about the electriccharacteristic from the sensor 120. The measurement value may be ananalog signal or a digital signal. The control unit 130 may prepare avoltage profile and optionally a current profile by using a plurality ofvoltage and current values obtained from the sensor 120.

The sensor 120 and the control unit 130 configure a battery managementsystem (BMS), and the BMS may be included in the secondary batterymanaging apparatus 100.

The BMS may be a typical BMS system in the art. However, the presentdisclosure is not limited thereto, and any system including componentsperforming the same functions as the sensor 120 and the control unit 130may be included in the scope of the BMS.

Meanwhile, the sensor 120 may not be a component of the BMS. In thiscase, the BMS may include the control unit 130 as an essential element,and the control unit 130 may be electrically coupled to the sensor 120in order to obtain a measurement value of the electric characteristicfrom the sensor 120.

The secondary battery managing apparatus 100 is electrically connectedto a load 140. The load 140 may be included in various kinds ofelectric-driven apparatuses and means an energy-consuming deviceincluded in an electric-driven apparatus operated with the electricenergy supplied when the secondary battery 110 is discharged. The loadmay be a rotation-driving device such as a motor, a power-convertingdevice such as an inverter, or the like, but the present disclosure isnot limited to specific kinds of loads.

The secondary battery managing apparatus 100 may further include astorage unit 160, selectively. The storage unit 160 is not speciallylimited if it may serve as a storage medium capable of recording anderasing information. For example, the storage unit 160 may be RAM, ROM,register, hard disk, optical recording medium or magnetic recordingmedium. The storage unit 160 may be connected to the control unit 130 soas to be accessed by the control unit 130 through, for example, a databus or the like. The storage unit 160 store and/or update and/or eraseand/or transmit program having various control logics executed by thecontrol unit 130 and/or data generated when the control logics areexecuted. The storage unit 160 may be divided into two or more logicunits and may also be included in the control unit 130, without anyrestriction.

The secondary battery managing apparatus 100 may further include adisplay unit 150, selectively. The display unit 150 is not speciallylimited if it may display information generated by the control unit 130as a graphic interface. For example, the display unit 150 may be aliquid crystal display, an LED display, an OLED display, an E-INKdisplay, a flexible display or the like. The display unit 150 may beconnected to the control unit 130 directly or indirectly. When indirectconnection is adopted, the display unit 150 may be located in an areaphysically separated from the area where the control unit 130 islocated. In addition, a third control unit (not shown) may be interposedbetween the display unit 150 and the control unit 130 to receiveinformation, which will be displayed on the display unit 150 by thethird control unit, from the control unit 130 and display theinformation on display unit 150. For this, the third control unit andthe control unit 130 may be connected through a communication line.

The control unit 130 is a component capable of executing at least onecontrol logic required for estimating a state of the secondary battery110 and may estimate a state of the secondary battery 110 by using apredetermined mathematical model, a look-up table or look-up function,or the like, without being limited thereto.

According to an embodiment, the control unit 130 may estimate a state ofthe secondary battery by using a predetermined voltage estimating model.Preferably, the voltage estimating model may be based on a circuitmodel.

The voltage estimating model is a mathematical model for estimating avoltage profile which may approximate a voltage profile measured by thesensor 120 after the secondary battery comes to an idle state or ano-load state and may be expressed as a generalized function as shown inEquation (1) below.V _(cell) =V _(cathode) [k]−V _(anode) [k]  (1)

In Equation (1), V_(cell)[k] represents an estimated voltage of thesecondary battery 110, V_(cathode)[k] represents an estimated voltageformed at the cathode of the secondary battery 110, and V_(anode)[k]represents an estimated voltage formed at the anode of the secondarybattery 110. In addition, k represents a time index corresponding to thetime when the voltage of the secondary battery 110 is measured. Forexample, if the profile of voltages measured by the sensor 120 hasvoltage data measured as much as 100 times, k has an integer valuebelonging to the range of 0 to 99 (including the borders). Hereinafter,unless otherwise noted, terms endowed with k in parenthesis representterms estimated or calculated at k^(th) times.

In an embodiment, V_(cathode)[k] and V_(anode)[k] may be expressed asgeneralized functions as shown in Equations (2) and (3) below.V _(cathode) [k]=f(V _(c1) [k],V _(c2) [k],i _(cell) [k],R ₀ _(_)_(relax), . . . )  (2)V _(anode) [k]=g(V _(a) [k],i _(cell) [k], . . . )  (3)

Here, V_(c1)[k], V_(c2)[k] and V_(a)[k] may be generalized as shown inEquations (4), (5) and (6), without being limited thereto.V _(c1) [k]=OCV _(c1)(z _(c1) [k])+V _(impedance) _(_) _(c1) [k]  (4)V _(c2) [k]=OCV _(c2)(z _(c2) [k])+V _(impedance) _(_) _(c2) [k]  (5)V _(a) [k]=OCV _(a)(z _(a) [k])+V _(impedance) _(_) _(a) [k]  (6)

In Equation (2), the function f represents a function for calculating avoltage of the cathode of the secondary battery 110, and in Equation(3), the function g represents a function for calculating a voltage ofthe anode of the secondary battery 110. These functions f and g may bederived from a circuit model as an embodiment, as being described laterin detail.

In the operation expressions shown in Equations (2) to (6), thesubscripts ‘c1’ and ‘c2’ respectively represent the first cathodematerial and the second cathode material included in the blended cathodematerial, and the subscript ‘a’ represents the anode material includedin the anode. In addition, the subscripts ‘impedance_c1’ and‘impedance_c2’ respectively represent impedance including a resistancecomponent, a capacity component, an inductor component or theircombinations, respectively originating from the first cathode materialand the second cathode material, and the impedance_a representsimpedance including a resistance component, a capacity component, aninductor component or their combinations, originating from the anodematerial.

Referring to Equation (2), the function f used for calculating theV_(cathode)[k] of the cathode includes at least V_(c1)[k], V_(c2)[k],i_(cell)[k] and R₀ _(_) _(relax) as input parameters. In addition, thefunction g used for calculating the V_(anode)[k] of the anode includesat least V_(a)[k] and i_(cell)[k] as input parameters. The symbol . . .′ included in the functions f and g shows that different parameters maybe added as input parameters when necessary.

In the functions f and g, i_(cell)[k] is a common parameter andrepresents current flowing through the secondary battery 110. Thei_(cell)[k] may be detected by the sensor 120. When the secondarybattery 110 is discharged, the i_(cell)[k] is a discharge current. Ifthe secondary battery 110 comes to an idle state or a no-load statewhile being discharged, the i_(cell)[k] becomes substantially 0 (zero)or decreases to a small negligible value.

The functions f and g include various parameters in addition toi_(cell)[k]. Hereinafter, the various parameters of each of the functionf and g will be taken into consideration.

<Input Parameters of the Function f>

In the function f, V_(c1)[k] is a voltage formed at the first cathodematerial as a result of reaction of the first cathode material andoperating ions and is expressed as a sum of at least OCV_(c1)(z_(c1)[k])and V_(impedance) _(_) _(c1)[k].

The OCV_(c1)(z_(c1)[k]) is an open-circuit voltage component of thefirst cathode material and changes according to z_(c1)[k] which is astate of the first cathode material. Since z_(c1)[k] decreases from 1 to0 as operating ions react with the first cathode material, theOCV_(c1)(z_(c1)[k]) tends to decrease as z_(c1)[k] decreases. TheOCV_(c1)(z_(c1)[k]) may be defined in advance by making a half cell withthe first cathode material and measuring an open-circuit voltage profileof the half cell while discharging the secondary battery until SOC(namely, z_(c1)[k]) changes from 1 to 0.

The OCV_(c1)(z_(c1)[k]) may be a look-up table built by storing anopen-circuit voltage of each z_(c1)[k] of the open-circuit voltageprofile as a table-type database, or a look-up function obtained bynumerically analyzing the open-circuit voltage profile as a function,without being limited thereto.

When an entire capacity of the first cathode material where operatingions may be intercalated is Q_(c1), if the operating ions start beingintercalated, the z_(c1)[k] decreases from 1 in inverse proportion to aratio of the capacity of intercalated operating ions in comparison tothe Q_(c1) and becomes 0 if all operating ions corresponding to theentire capacity Q₁ are intercalated into the first cathode material. Inother words, the z_(c1)[k] is a parameter inversely proportional to theamount of operating ions having reacted with the first cathode materialand may correspond to SOC of the half cell of the first cathode materialmentioned above. Therefore, the z_(c1)[k] may be regarded as a parameterrepresenting a state of the first cathode material.

The V_(impedance) _(_) _(c1)[k] represents a voltage component formed byimpedance including a resistance component, a capacity component, aninductor component or their combinations, originating from the firstcathode material. The impedance may be changed according to the kind ofthe first cathode material, and if there is no impedance in view of theelectrochemical characteristic of the first cathode material, it is notexcluded that the V_(impedance) _(_) _(c1)[k] becomes 0. In addition, atleast two component included in the impedance may be connected in seriesand/or in parallel. In addition, the V_(impedance) _(_) _(c1)[k] ischanged with the influence of current generated when the first cathodematerial reacts with operating ions. Therefore, the V_(impedance) _(_)_(c1)[k] may be calculated by using an impedance voltage calculationequation derived from a common circuit theory.

In addition, in the function f, V_(c2)[k] is a voltage formed at thesecond cathode material as a result of reaction between the secondcathode material and operating ions and is expressed as a sum of atleast OCV_(c2)(z_(c2)[k]) and V_(impedance) _(_) _(c2)[k].

The OCV_(c2)(z_(c2)[k]) is an open-circuit voltage component of thesecond cathode material and changes according to z_(c2)[k] which is astate of the second cathode material. Since z_(c2)[k] decreases from 1to 0 as operating ions react with the second cathode material, theOCV_(c2)(z_(c2)[k]) tends to decrease as z_(c2)[k] decreases. TheOCV_(c2)(z_(c2)[k]) may be defined in advance by making a half cell withthe second cathode material and measuring an open-circuit voltageprofile of the half cell while discharging the secondary battery untilSOC (namely, z_(c2)[k]) changes from 1 to 0.

The OCV_(c2)(z_(c2)[k]) may be a look-up table built by storing anopen-circuit voltage of each z_(c2)[k] of the open-circuit voltageprofile as a table-type database, or a look-up function obtained bynumerically analyzing the open-circuit voltage profile as a function,without being limited thereto.

When an entire capacity of the second cathode material where operatingions may be intercalated is Q_(c2), if the operating ions start beingintercalated, the z_(c2)[k] decreases from 1 in inverse proportion to aratio of the capacity of intercalated operating ions in comparison tothe Q_(c2) and becomes 0 if all operating ions corresponding to theentire capacity Q_(c2), are intercalated into the secondary cathodematerial. In other words, the z_(c2)[k] is a parameter inverselyproportional to the amount of operating ions having reacted with thesecond cathode material and may correspond to SOC of the half cell ofthe second cathode material mentioned above. Therefore, the z_(c2)[k]may be regarded as a parameter representing a state of the secondcathode material.

The V_(impedance) _(_) _(c2)[k] represents a voltage component formed byimpedance including a resistance component, a capacity component, aninductor component or their combinations, originating from the secondcathode material. The impedance may be changed according to the kind ofthe second cathode material, and if there is no impedance in view of theelectrochemical characteristic of the second cathode material, it is notexcluded that the V_(impedance) _(_) _(c2)[k] becomes 0. In addition, atleast two component included in the impedance may be connected in seriesand/or in parallel. In addition, the V_(impedance) _(_) _(c2)[k] ischanged with the influence of current generated when the second cathodematerial reacts with operating ions. Therefore, the V_(impedance) _(_)_(c2)[k] may be calculated by using an impedance voltage calculationequation derived from a common circuit theory.

R₀ _(_) _(relax) which is another input parameter included in thefunction f, represents a resistance component which disturbs movement ofoperating ions while the operating ions are transferred between thecathode materials when voltage relaxation occurs in the blended cathodematerial. In other words, since the transfer of operating ions in thecathode materials may be equivalently analyzed with the current flow, R₀_(_) _(relax) may be regarded as representing a series resistancecomponent present on the path of current in view of an electric circuit.

Since the R₀ _(_) _(relax) is changed according to an amount ofoperating ions intercalated into the first and second cathode materials,the behavior of the R₀ _(_) _(relax) may be described as follows on theassumption that the first and second cathode materials are respectivelya receiver and a donor of operating ions.

Since the R₀ _(_) _(relax) corresponds to a resistance componentdisturbing movement of operating ions in an electric aspect, if theresistance component increases, the time taken for completing thetransfer of operating ions, namely a voltage relaxation time, increases.Here, the voltage relaxation time is defined as τ_(relax) of FIG. 9.Therefore, a factor which increases the voltage relaxation timeτ_(relax) acts as a factor which increases the magnitude of R₀ _(_)_(relax,) and on the contrary, a factor which decreases the voltagerelaxation time τ_(relax) acts as a factor which decreases the magnitudeof R₀ _(_) _(relax).

In detail, when the secondary battery comes to an idle state or ano-load state (namely, k=0) in the intrinsic voltage range where voltagerelaxation is possible, if the amount of operating ions intercalatedinto the second cathode material is sufficiently large, the amount ofoperating ions to be transferred to the first cathode material increasesas much, which results in the increase of the voltage relaxation timeτ_(relax). Therefore, when the secondary battery comes to an idle stateor a no-load state, as the capacity of operating ions intercalated intothe second cathode material is greater, namely, as z_(c2)[0] is smaller,the magnitude of R₀ _(_) _(relax) increases, or vice versa. In addition,when the secondary battery comes to an idle state or a no-load state(namely, k=0) in the intrinsic voltage range where voltage relaxation ispossible, a residual capacity of the first cathode material whereoperating ions may be intercalated gives an influence on the magnitudeof R₀ _(_) _(relax). In other words, if the residual capacity of thefirst cathode material where operating ions may be intercalated islarge, operating ions are transferred that much faster, which shortensthe voltage relaxation time τ_(relax). Therefore, as a residual capacityof the first cathode material where operating ions may be intercalatedis greater, namely as z_(c1)[0] is greater, the size of R₀ _(_) _(relax)decreases, or vice versa. If taking such behavior of R₀ _(_) _(relax)into consideration, R₀ _(_) _(relax) may be estimated from a parametergenerally expressed by Equation (7) below, without being limitedthereto.

$\begin{matrix}\frac{\left( {1 - {z_{C\; 2}\lbrack 0\rbrack}} \right)Q_{C\; 1}}{{z_{C\; 1}\lbrack 0\rbrack}Q_{C\; 2}} & (7)\end{matrix}$

<Input Parameters of the Function g>

In the function g, V_(a)[k] is a voltage formed at the anode material asa result of the reaction of the anode material and operating ions and isexpressed as a sum of at least OCV_(a)(z_(a)[k]) and V_(impedance) _(_)_(a)[k].

The OCV_(a)(z_(a)[k]) is an open-circuit voltage component of the anodematerial and changes according to z_(a)[k] which is a state of the anodematerial. z_(a)[k] decreases as a state of the anode material decreases,namely operating ions are deintercalated from the anode material. Forreference, in view of the anode material, the decrease of a state meansthat operating ions are deintercalated from the anode material.Therefore, OCV_(a)(z_(a)[k]) tends to increase as z_(a)[k] decreases.The OCV_(a)(z_(a)[k]) may be defined by using an open-circuit voltageprofile obtained by making a half cell with the anode material andmeasuring an open-circuit voltage while varying SOC (namely, z_(a)[k])of the half cell from 1 to 0.

The OCV_(a)(z_(a)[k]) may be a look-up table built by storing anopen-circuit voltage of each z_(a)[k] of the open-circuit voltageprofile as a table-type database, or a look-up function obtained bynumerically analyzing the open-circuit voltage profile as a function,without being limited thereto.

When an entire capacity of the anode material where operating ions maybe deintercalated is Q_(a), if the operating ions start beingdeintercalated, the z_(a)[k] decreases from 1 in inverse proportion to aratio of the capacity of deintercalated operating ions in comparison tothe Q_(a) and becomes 0 if all operating ions corresponding to theentire capacity Q_(a) are deintercalated from the anode material. Inother words, the z_(a)[k] is a parameter inversely proportional to theamount of operating ions deintercalated from the anode material and maycorrespond to SOC of the half cell of the anode material mentionedabove. In addition, since the ratio of operating ions deintercalatedfrom the anode material is identical to the state of the secondarybattery, the z_(a)[k] may correspond to z_(cell)[k] which is a parameterrepresenting a state of the secondary battery.

The V_(impedance) _(_) _(a)[k] represents a voltage component formed byimpedance including a resistance component, a capacity component, aninductor component or their combinations, originating from the anodematerial. The impedance may be changed according to the kind of theanode material, and if there is no impedance in view of theelectrochemical characteristic of the anode material, it is not excludedthat the v_(impedance) _(_) _(a)[k] becomes 0. In addition, at least twocomponent included in the impedance may be connected in series and/or inparallel. In addition, the v_(impedance) _(_) _(a)[k] is changed withthe influence of current generated when the anode material reacts withoperating ions. Therefore, the V_(impedance) _(_) _(a)[k] may becalculated by using an impedance voltage calculation equation derivedfrom a common circuit theory.

From the above equations, V_(cell)[k], V_(c1)[k], V_(c2)[k] and V_(a)[k]may be arranged again as shown in Equations (8), (9), 10 and (11) below.V _(cell) [k]=f(V _(c1) [k],V _(c2) [k],i _(cell) [k],R ₀ _(_) _(relax),. . . )−g(V _(a) [k], . . . )  (8)V _(c1) [k]=OCV _(c1)(z _(c1) [k])+V _(impedance) _(_) _(c1) [k]  (9)V _(c2) [k]=OCV _(c2)(z _(c2) [k])+V _(impedance) _(_) _(c2) [k]  (10)V _(a) [k]=OCV _(a)(z _(a) [k])+V _(impedance) _(_) _(a) [k]  (11)

Hereinafter, a voltage estimating model capable of being derived from acircuit model will be described as a more detailed embodiment. However,the present disclosure is not limited to the embodiment. Meanwhile, thecircuit model capable of being used for deriving the voltage estimatingmodel may be modified when necessary according to the kind of blendedcathode material included in the secondary battery. Therefore, eventhough the circuit model is modified according to the modification ofthe blended cathode material, the modified circuit model should beincluded in the scope of the circuit model disclosed in the presentdisclosure.

FIG. 11 is a circuit diagram exemplarily showing a circuit model 200capable of inducing a voltage estimating model according to anembodiment of the present disclosure.

Referring to FIG. 11, the circuit model 200 includes an anode circuitunit 210 and a cathode circuit unit 220, and the cathode circuit unit220 includes at least a first cathode material circuit unit 221 and asecond cathode material circuit unit 222.

The anode circuit unit 210 includes an open-circuit voltage component210 a of the anode material and an impedance component 210 b relating toelectrochemical properties of the anode material. When the secondarybattery is discharged, voltage differences respectively corresponding toOCV_(a)(z_(a)[k]) and V_(impedance) _(_) _(a)[k] are generated at bothterminals of the open-circuit voltage component 210 a and the impedancecomponent 210 b of the anode material. The OCV_(a)(z_(a)[k]) andV_(impedance) _(_) _(a)[k] have been described above with reference toEquation (11).

In an embodiment, the impedance component 210 b of the anode materialincludes an RC circuit having a resistance component R_(a) and acapacity component C_(a) connected in parallel as circuit components,and a resistance component R₀ _(_) _(a) connected to the RC circuit inseries. The resistance component R_(a) and R₀ _(_) _(a) and the capacitycomponent C_(a) included in the impedance component 210 b of the anodematerial are determined by experiments considering electrochemicalproperties of at least an anode material and electric properties of ametallic current collector included in the anode. In addition, theresistance component and/or capacity component included in the impedancecomponent 210 b of the anode material may be omitted. In addition, theimpedance component 210 b of the anode material may further includeanother resistance component, another capacity component, anotherinductor component, or combinations thereof.

The first cathode material circuit unit 221 includes an open-circuitvoltage component 221 a of the first cathode material and an impedancecomponent 221 b of the first cathode material. When the secondarybattery is discharged, voltage differences corresponding toOCV_(c1)(z_(c1)[k]) and V_(impedance) _(_) _(c1)[k] are respectivelygenerated at both ends of the open-circuit voltage component 221 a andthe impedance component 221 b of the first cathode material. TheOCV_(c1)(z_(c1)[k]) and V_(impedance) _(_) _(c1)[k] have been describedabove with reference to Equation (9).

In an embodiment, the impedance component 221 b of the first cathodematerial includes an RC circuit having a resistance component R_(c1) anda capacity component C_(c1) connected in parallel as circuit components,and a resistance component R₀ _(_) _(c1) connected to the RC circuit inseries. The resistance components R_(c1) and R₀ _(_) _(c1) and thecapacity component C_(c1) included in the impedance component 221 b ofthe first cathode material are determined by experiments consideringelectrochemical properties of at least a first cathode material andelectric properties of a metallic current collector included in thecathode. In addition, the resistance component and/or capacity componentincluded in the impedance component 221 b of the first cathode materialmay be omitted. In addition, the impedance component 221 b of the firstcathode material may further include another resistance component,another capacity component, another inductor component, or combinationsthereof.

The second cathode material circuit unit 222 includes an open-circuitvoltage component 222 a and an impedance component 222 b of the secondcathode material. When the secondary battery is discharged, voltagedifferences respectively corresponding to OCV_(c2)(z_(c2)[k]) andV_(impedance) _(_) _(c2)[k] are generated at both ends of theopen-circuit voltage component 222 a and the impedance component 222 bof the second cathode material. The OCV_(c2)(z_(c2)[k]) andV_(impedance) _(_) _(c2)[k] have been described above with reference toEquation (10).

In an embodiment, the impedance component 222 b of the second cathodematerial includes an RC circuit having a resistance component R_(c2) anda capacity component C_(c2) connected in parallel as circuit components,and a resistance component R₀ _(_) _(c2) connected to the RC circuit inseries. The resistance components R_(c2) and R₀ _(_) _(c2) and thecapacity component C_(c2) included in the impedance component 222 b ofthe second cathode material are determined by experiments consideringelectrochemical properties of at least a second cathode material andelectric properties of a metallic current collector included in thecathode. In addition, the resistance component and/or capacity componentincluded in the impedance component 222 b of the second cathode materialmay be omitted. In addition, the impedance component 222 b of the secondcathode material may further include another resistance component,another capacity component, another inductor component, or combinationsthereof.

Meanwhile, while the secondary battery is being discharged, operatingions are deintercalated from the anode material included in the anodeand move to the blended cathode material included in the cathode. Themovement of operating ions may be expressed by current flow i_(cell),i_(c1), i_(c2) at the circuit model 200. A single operating ion movingfrom the anode to the cathode during the discharge of the secondarybattery reacts with either the first cathode material or the secondcathode material. Therefore, the current flowing form the anode to thecathode is divided into a current i_(c1) flowing toward the firstcathode material and a current i_(c2), flowing toward the second cathodematerial. The current division is shown at a parallel circuit.Therefore, in the circuit model 200, the first cathode material circuitunit 221 and the second cathode material circuit unit 222 are connectedin parallel. However, the electric connection between the first cathodematerial and the second cathode material in the circuit model may bemodified in various ways according to the kind of cathode materials ofthe blended cathode material and an operating mechanism of the secondarybattery, as obvious in the art.

In the anode, since the current flowing to the cathode corresponds tothe entire current flowing in the secondary battery while the secondarybattery is being discharged, the magnitude of the current is identicalto the magnitude of i_(cell)[k] which is a discharge current of thesecondary battery. Therefore, a current equation may be induced based onthe node n shown in the circuit model, like Equation (12) below.−i _(cell) [k]=i _(c1) [k]+i _(c2) [k]  (12)

In Equation (12), when the secondary battery is being charged,i_(cell)[k] has a negative value and i_(c1)[k] and i_(c2)[k] havepositive values. On the contrary, when the secondary battery is beingdischarged, i_(cell)[k] has a positive value and i_(c1)[k] and i_(c2)[k]have negative values.

Meanwhile, when a voltage difference of both ends of the resistancecomponent R₀ _(_) _(c1) is defined as V_(R0) _(_) _(c1)[k] and a voltagedifference of both ends of the resistance component R₀ _(_) _(c2) isdefined as V_(R0) _(_) _(c2)[k], due to the Ohm's low, i_(c1)[k] andi_(a)[k] of Equation (12) may be arranged as shown in Equations (13) and(14) below

$\begin{matrix}{{i_{c\; 1}\lbrack k\rbrack} = \frac{V_{R\; 0{\_ C}\; 1}\lbrack k\rbrack}{R_{0{\_ C}\; 1}}} & (13) \\{{i_{c\; 2}\lbrack k\rbrack} = \frac{V_{R\; 0{\_ C}\; 2}\lbrack k\rbrack}{R_{0{\_ C}\; 2}}} & (14)\end{matrix}$

In addition, if voltages applied to left terminals of the resistancecomponents R₀ _(_) _(c1) and R₀ _(_) _(c2) are respectively defined asV*_(c1)[k] and V*_(c2)[k] and a voltage applied to the cathode terminalis defined as V_(cathode)[k], V_(R0) _(_) _(c1)[k] and V_(R0) _(_)^(c2)[k] of Equations (13) and (14) may be respectively arranged likeEquations (15) and (16) below.V _(R0) _(_) _(c1) [k]=V _(cathode) [k]−V* _(c1) [k]  (15)V _(R0) _(_) _(c2) [k]=V _(cathode) [k]−V* _(c2) [k]  (16)

If Equations (13), (14), (15) and (16) are applied to Equation (12),Equation (12) may be arranged like Equation (17) below.

$\begin{matrix}{\begin{matrix}{{- {i_{cell}\lbrack k\rbrack}} = {{i_{c\; 1}\lbrack k\rbrack} + {i_{c\; 2}\lbrack k\rbrack}}} \\{= {\frac{{V_{cathode}\lbrack k\rbrack} - {V_{C\; 1}^{*}\lbrack k\rbrack}}{R_{0_{C\; 1}}} + \frac{{V_{cathode}\lbrack k\rbrack} - {V_{C\; 2}^{*}\lbrack k\rbrack}}{R_{0_{C\; 2}}}}}\end{matrix}{{V_{cathode}\left( {\frac{1}{R_{0{\_ C}\; 1}} + \frac{1}{R_{0{\_ C}\; 2}}} \right)} = {\frac{V_{C\; 1}^{*}\lbrack k\rbrack}{R_{0{\_ C}\; 1}} + \frac{V_{C\; 2}^{*}\lbrack k\rbrack}{R_{0{\_ C}\; 2}} - {i_{cell}\lbrack k\rbrack}}}{V_{cathode} = {\left( \frac{R_{0{\_ C}\; 1}R_{0{\_ C}\; 2}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}} \right)\left( {\frac{V_{C\; 1}^{*}\lbrack k\rbrack}{R_{0{\_ C}\; 1}} + \frac{V_{C\; 2}^{*}\lbrack k\rbrack}{R_{0{\_ C}\; 2}} - {i_{cell}\lbrack k\rbrack}} \right)}}} & (17)\end{matrix}$

In addition, if Equations (15), (16) and (17) are applied to Equations(13) and (14), Equations (13) and (14) may be arranged like Equations(18) and (19) below.

$\begin{matrix}{{{i_{c\; 1}\lbrack k\rbrack} = \frac{{V_{cathode}\lbrack k\rbrack} - {V_{C\; 1}^{*}\lbrack k\rbrack}}{R_{0{\_ C}\; 1}}}{{i_{c\; 1}\lbrack k\rbrack} = \frac{{V_{C\; 2}^{*}\lbrack k\rbrack} - {V_{C\; 1}^{*}\lbrack k\rbrack} - {{i_{cell}\lbrack k\rbrack}R_{0{\_ C}\; 2}}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}}}} & (18) \\{{{i_{c\; 2}\lbrack k\rbrack} = \frac{{V_{cathode}\lbrack k\rbrack} - {V_{C\; 2}^{*}\lbrack k\rbrack}}{R_{0{\_ C}\; 2}}}{{i_{c\; 2}\lbrack k\rbrack} = \frac{{V_{C\; 1}^{*}\lbrack k\rbrack} - {V_{C\; 2}^{*}\lbrack k\rbrack} - {{i_{cell}\lbrack k\rbrack}R_{0{\_ C}\; 1}}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}}}} & (19)\end{matrix}$

Meanwhile, if considering the node n connecting the first and secondcathode materials circuit units 221, 222 as a reference potential,V*_(c1)[k] and V*_(c2)[k] may be expressed like Equations (20) and (21)below.V* _(c1) [k]=OCV _(c1)(z _(c1) [k])+V _(RC) _(_) _(c1) [k]  (20)V* _(c2) [k]=OCV _(c2)(z _(c2) [k])+V _(RC) _(_) _(c2) [k]  (21)

In Equation (20), OCV_(c1)(z_(c1)[k]) is a voltage formed by theopen-circuit voltage component 221 a of the first cathode material, andV_(RC) _(_) _(c1)[k] is a voltage formed by the RC circuit included inthe impedance component 221 b of the first cathode material. Similarly,in Equation (21), OCV_(c2)(z_(c2)[k]) is a voltage formed by theopen-circuit voltage component 222 a of the second cathode material, andV_(RC) _(_) _(c2)[k] is a voltage formed by the RC circuit included inthe impedance component 222 b of the second cathode material.

By using Equations (20) and (21), Equations (17), (18) and (19) may bearranged like Equations (22), (23) and (24) below.

$\begin{matrix}{{V_{cathode}\lbrack k\rbrack} = {\left( \frac{R_{0{\_ C}\; 1}R_{0{\_ C}\; 2}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}} \right)\begin{pmatrix}{\frac{\left. {{{OCV}_{C\; 1}\left( {z_{C\; 1}\lbrack k\rbrack} \right)} + {V_{{{RC}\_ C}\; 1}\lbrack k\rbrack}} \right)}{R_{0_{C\; 1}}} +} \\{\frac{{{OCV}_{C\; 2}\left( {z_{C\; 2}\lbrack k\rbrack} \right)} + {V_{{{RC}\_ C}\; 2}\lbrack k\rbrack}}{R_{0_{C\; 2}}} -} \\{i_{cell}\lbrack k\rbrack}\end{pmatrix}}} & (22) \\{\mspace{79mu}{{i_{c\; 1}\lbrack k\rbrack} = \frac{\begin{matrix}{\left( {{{OCV}_{C\; 2}\left( {z_{C\; 2}\lbrack k\rbrack} \right)} + {V_{{{RC}\_ C}\; 2}\lbrack k\rbrack}} \right) -} \\{\left( {{{OCV}_{C\; 1}\left( {z_{C\; 1}\lbrack k\rbrack} \right)} + {V_{{{RC}\_ C}\; 1}\lbrack k\rbrack}} \right) -} \\{{i_{cell}\lbrack k\rbrack}R_{0{\_ C}\; 2}}\end{matrix}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}}}} & (23) \\{\mspace{79mu}{{i_{c\; 2}\lbrack k\rbrack} = \frac{\begin{matrix}{\left( {{{OCV}_{C\; 1}\left( {z_{C\; 1}\lbrack k\rbrack} \right)} + {V_{{{RC}\_ C}\; 1}\lbrack k\rbrack}} \right) -} \\{\left( {{{OCV}_{C\; 2}\left( {z_{C\; 2}\lbrack k\rbrack} \right)} + {V_{{{RC}\_ C}\; 2}\lbrack k\rbrack}} \right) -} \\{{i_{cell}\lbrack k\rbrack}R_{0{\_ C}\; 1}}\end{matrix}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}}}} & (24)\end{matrix}$

In Equations (22), (23) and (24), V_(RC) _(_) _(c1)[k] and V_(RC) _(_)_(c2)[k] are voltages respectively formed at the RC circuits of thefirst and second cathode material circuit units 221, 222. Generally,voltage and current of the RC circuit satisfy Differential Equation (25)below as time t changes. Therefore, if Equation (25) is changed into adiscrete time equation, Equation (26) below may be obtained, where Δtrepresents a current and voltage measurement interval.

$\begin{matrix}{{\overset{.}{V}(t)} = {{{- \frac{1}{RC}}{V(t)}} + {\frac{1}{c}{i(t)}}}} & (25) \\{{V\left\lbrack {k + 1} \right\rbrack} = {{{V\lbrack k\rbrack}e^{- \frac{\Delta\; t}{RC}}} + {{R\left( {1 - e^{- \frac{\Delta\; t}{RC}}} \right)}{i\lbrack k\rbrack}}}} & (26)\end{matrix}$

If Equation (26) corresponding to an RC circuit equation is used, thevoltages V_(RC) _(_) _(c1)[k] and V_(RC) _(_) _(c2)[k] respectivelyformed by RC circuits of the first and second cathode materials circuitunits 221, 222 may be expressed with a discrete time equation likeEquations (27) and (28) below.

$\begin{matrix}{{V_{{{RC}\_ c}\; 1}\left\lbrack {k + 1} \right\rbrack} = {{{V_{{{RC}\_ c}\; 1}\lbrack k\rbrack}e^{- \frac{\Delta\; t}{R_{C\; 1}C_{C\; 1}}}} + {{R_{c\; 1}\left( {1 - e^{- \frac{\Delta\; t}{R_{C\; 1}C_{C\; 1}}}} \right)}{i_{c\; 1}\lbrack k\rbrack}}}} & (27) \\{{V_{{{RC}\_ c}\; 2}\left\lbrack {k + 1} \right\rbrack} = {{{V_{{{RC}\_ c}\; 2}\lbrack k\rbrack}e^{- \frac{\Delta\; t}{R_{C\; 1}C_{C\; 2}}}} + {{R_{c\; 2}\left( {1 - e^{- \frac{\Delta\; t}{R_{C\; 2}C_{C\; 2}}}} \right)}{i_{c\; 2}\lbrack k\rbrack}}}} & (28)\end{matrix}$

Equation (27) is a voltage calculation equation for calculating avoltage formed by the RC circuit among impedance components included inthe first cathode material circuit unit 221. The impedance of the firstcathode material circuit unit 221 further includes a resistance R₀ _(_)_(c1). Therefore, the impedance voltage calculation equation forcalculating a voltage formed by the impedance of the first cathodematerial circuit unit 221 may be induced by adding voltage R₀ _(_)_(c1)·i_(c1)[k] formed by resistance R₀ _(_) _(c1) to Equation (27).

In addition, Equation (28) is a voltage calculation equation forcalculating a voltage formed by the RC circuit among impedancecomponents included in the second cathode material circuit unit 222. Theimpedance of the second cathode material circuit unit 222 furtherincludes a resistance R₀ _(_) _(c2). Therefore, the impedance voltagecalculation equation for calculating a voltage formed by the impedanceof the second cathode material circuit unit 222 may be induced by addingvoltage R₀ _(_) _(c2)·i_(c2)[k] formed by resistance R₀ _(_) _(c2) toEquation (28).

Meanwhile, referring to Equation (22), the voltage V_(cathode)[k] of thecathode terminal is determined by four variables, namely voltagesOCV_(c1)(z_(c1)[k]) and OCV_(c2)(z_(c2)[k]) formed by the open-circuitvoltage component of the first and second cathode materials circuitunits 221, 222 and voltages V_(RC) _(_) _(c1)[k] and V_(RC) _(_)_(c2)[k] formed by the RC circuit.

Among the four variables, OCV_(c1)(z_(c1)[k]) and OCV_(c2)(z_(c2)[k])corresponding to z_(c1)[k] and z_(c2)[k] may be defined in advance as alook-up table or a look-up function as described above. Therefore,OCV_(c1)(z_(c1)[k]) and OCV_(c2)(z_(c2)[k]) may be calculated instantlyif z_(c1)[k] and z_(c2)[k] are known.

The z_(c1)[k] and z_(c2)[k] is changed according to i_(c1)[k] andi_(c1)[k] which are currents respectively flowing to the first andsecond cathode materials during Δt. Therefore, discrete time equationsrelating to the z_(c1)[k] and z_(c2)[k] may be expressed like Equations(29) and (30) below.z _(c1) [k+1]=z _(c1) [k]+i _(c1) [k]Δt/Q _(c1)  (29)z _(c2) [k+1]=z _(c2) [k]+i _(c2) [k]Δt/Q _(c2)  (30)

In the above, in order to calculate the voltage V_(cathode)[k] of thecathode terminal by using Equations (27), (28), (29) and (30) which arefour discrete time equations induced as above, it is required toinitialize V_(RC) _(_) _(c1)[0], V_(RC) _(_) _(c2)[0], z_(c1)[0],z_(c2)[0], i_(c1)[0], i_(c2)[0] to specific values when k is 0 (zero).However, referring to Equations (23) and (24), since i_(c1)[0] andi_(c2)[0] are eventually determined by V_(RC) _(_) _(c1)[0], V_(RC) _(_)_(c2)[0], z_(c1)[0] and z_(c2)[0], the values to be initialized arereduced to V_(RC) _(_) _(c1)[0] V_(RC) _(_) _(c2)[0], z_(c1)[0] andz_(c2)[0].

Among the values required to be initialized, V_(RC) _(_) _(c1)[0] andV_(RC) _(_) _(c2)[0] are voltages formed at the RC circuits included inthe first and second cathode materials circuit units 221, 222 after thesecondary battery comes to an idle state or a no-load state. However, inthe RC circuit, voltage changes slowly even though current flows throughthe RC circuit. Therefore, in an embodiment, the V_(RC) _(_) _(c1)[0]and V_(RC) _(_) _(c2)[0] may be set to have initial condition values of0 (zero) as shown in Equations (31) and (32) below. Of course, V_(RC)_(_) _(c1)[0] and V_(RC) _(_) _(c2)[0] may be set to have values greaterthan 0 (zero) depending on the kinds of the blended cathode materialincluded in the secondary battery.V _(RC) _(_) _(c1)[0]=0  (31)V _(RC) _(_) _(c2)[0]=0  (32)

As described above, if V_(RC) _(_) _(c1)[0] and V_(RC) _(_) _(c2)[0] areinitialized, the impedance voltage components V_(impedance) _(_)_(c1)[k] and V_(impedance) _(_) _(c2)[k] included in the first cathodematerial circuit unit 221 and the second cathode material circuit unit222 may be respectively initialized to R₀ _(_) _(c1)·i_(c1)[0] and R₀_(_) _(c2)·i_(c2)[0].

In addition, z_(c1)[0] and z_(c2)[0] exhibits residual capacities of thefirst and second cathode materials where operating ions may beintercalated, when the secondary battery comes to an idle state or ano-load state. The z_(c1)[0] and z_(c2)[0] may be initialized to valuesof OCV⁻¹ _(c1) (OCV_(c1)[0]) and OCV⁻¹ _(c2) (OCV_(c2)[0]). Here, OCV⁻¹_(c1) and OCV⁻¹ _(c1) correspond to an inversely transformed look-uptable or an inversely transformed look-up function ofOCV_(c1)(z_(c1)[k]) and OCV_(c2)(z_(c2)[k]), which may be defined inadvance. Therefore, the OCV⁻¹ _(c1) and OCV⁻¹ _(c1) may be regarded asoperators for calculating states z_(c1)[0] and z_(c2)[0] of the firstand second cathode materials, which may respectively correspond tovoltages OCV_(c1)[0] and OCV_(c2)[0] formed at the open-circuit voltagecomponents of the first and second cathode materials circuit units.

Meanwhile, just after the secondary battery comes to an idle state or ano-load state, the values of OCV_(c1)[0] and OCV_(c2)[0] may not beexactly recognized. Therefore, in an embodiment, the OCV_(c1)[0] andOCV_(c2)[0] may be approximately set like Equations (33) and (34) belowby using voltage V_(cell)[0] of the secondary battery, measured justafter the secondary battery comes to an idle state or a no-load state.However, Equations (33) and (34) may be modified when necessaryaccording to the kinds of the blended cathode material included in thesecondary battery and the operating mechanism of the secondary battery.Supposing V _(cell)[0]≅OCV _(c1)(z _(c1)[0])−OCV _(a)(z _(a)[0])OCV _(c1)(z _(c1)[0])≅V _(cell)[0], z _(a)[0]=z _(cell)[0],OCV _(c1)[0]=≅V _(cell)[0]+OCV _(a)(z _(cell)[0])  (33)Supposing V _(cell)[0]≅OCV _(c2)(z _(c2)[0])−OCV _(a)(z _(a)[0])OCV _(c2)(z _(c2)[0])≅V _(cell)[0], z _(a)[0]=z _(cell)[0],OCV _(c2)[0]≅V _(cell)[0]+OCV _(a)(z _(cell)[0])  (34)

In Equations (33) and (34), z_(cell)[0] may be calculated by usinginversely transformed OCV⁻¹ _(cell) of OCV_(cell) corresponding to alook-up table or a look-up function where an open-circuit voltage of thesecondary battery is defined according to a state of the secondarybattery. In other words, z_(cell)[0] is OCV_(cell) ⁻¹ (V_(cell)[0]). Thelook-up table or the look-up function of OCV_(cell) may be easilyobtained through an open-circuit voltage measurement experiment for eachstate of the secondary battery including the blended cathode material.In addition, OCV_(a) is a look-up table or a look-up function forcalculating a voltage formed at the open-circuit voltage component ofthe anode material circuit unit 210 by using a state of the anodematerial, namely a residual capacity of the anode material whereoperating ions may be deintercalated therefrom as an input parameter.This has been described in detail above with reference to Equation (11).

If Equations (33) and (34) are used, initial values of z_(c1) and z_(a)may be set as in Equations (35) and (36) below.z _(c1)[0]=OCV ⁻¹ _(c1)(OCV _(c1)[0])=OCV ⁻¹ _(c1)(V _(cell)[0]+OCV_(a)(OCV _(cell) ⁻¹(OCV _(cell)[0])))  (35)z _(c2)[0]=OCV ⁻¹ _(c2)(OCV _(c2)[0])=OCV ⁻¹ _(c2)(V _(cell)[0]+OCV_(a)(OCV _(cell) ⁻¹(V _(cell)[0])))  (36)

The voltage estimating model described above is focused on estimation ofa cathode voltage of the secondary battery including the blended cathodematerial. However, the above voltage estimating model may also besimilarly applied when estimating an anode voltage of the secondarybattery.

In other words, in the anode material circuit unit 210 of FIG. 11, whentaking the node n as a reference potential, voltage V*_(a)[k] applied tothe left terminal of the resistance R₀ _(_) _(a) may be expressed as asum of voltages formed at the open-circuit voltage component of theanode material circuit unit 210 and the RC circuit as shown in Equation(37) below.V* _(a) [k]=OCV _(a)(z _(a) [k])+V _(RC) _(_) _(a) [k]  (37)

In addition, since the voltage V_(anode)[k] of the anode terminal islower than V*_(a)[k] as much as i_(cell)[k]R₀ _(_) _(a), V_(anode)[k]may be expressed like Equation (38) below.

$\begin{matrix}\begin{matrix}{{V_{anode}\lbrack k\rbrack} = {{V_{a}^{*}\lbrack k\rbrack} - {{i_{cell}\lbrack k\rbrack}R_{0{\_ a}}}}} \\{= {{{OCV}_{a}\left( {z_{a}\lbrack k\rbrack} \right)} + {V_{{RC}\_ a}\lbrack k\rbrack} - {{i_{cell}\lbrack k\rbrack}R_{0{\_ a}}}}}\end{matrix} & (38)\end{matrix}$

In addition, a state z_(a)[k] of the anode material and a voltageapplied to the RC circuit of the anode material circuit unit 210 may beexpressed as discrete time equations like Equations (39) and (40) below,similar to Equations (27) and (29).

$\begin{matrix}\begin{matrix}{{z_{a}\left\lbrack {k + 1} \right\rbrack} = {{z_{a}\lbrack k\rbrack} - {{i_{a}\lbrack k\rbrack}\Delta\;{t/Q_{a}}}}} \\{= {{z_{a}\lbrack k\rbrack} - {{i_{cell}\lbrack k\rbrack}\Delta\;{t/Q_{a}}}}}\end{matrix} & (39) \\\begin{matrix}{{V_{{RC}\_ a}\left\lbrack {k + 1} \right\rbrack} = {{{V_{{RC}\_ a}\lbrack k\rbrack}e^{- \frac{\Delta\; t}{R_{a}C_{a}}}} + {{R_{a}\left( {1 - e^{- \frac{\Delta\; t}{R_{a}C_{a}}}} \right)}{i_{a}\lbrack k\rbrack}}}} \\{= {{{V_{{RC}\_ a}\lbrack k\rbrack}e^{- \frac{\Delta\; t}{R_{a}C_{a}}}} + {{R_{a}\left( {1 - e^{- \frac{\Delta\; t}{R_{a}C_{a}}}} \right)}{i_{cell}\lbrack k\rbrack}}}}\end{matrix} & (40)\end{matrix}$

Equation (40) is a voltage calculation equation formed by the RCcircuit, among the impedance components included in the anode materialcircuit unit 210. The impedance of the anode material circuit unit 210further includes resistance R₀ _(_) _(a). Therefore, the impedancevoltage calculation equation for calculating a voltage formed by theimpedance of the anode material circuit unit 210 may be induced byadding voltage R₀ _(_) _(a)·i_(cell)[k] formed by resistance R₀ _(_)_(a) to Equation (40).

In addition, in order to use the discrete time equations (39) and (40),in an embodiment, initial conditions V_(RC) _(_) _(a)[0] and z_(a)[0]may be set as in Equations (41) and (42).V _(RC) _(_) _(a)[0]=0  (41)z _(a)[0]=z _(cell)[0]=OCV ⁻¹ _(cell)(V _(cell)[0])  (42)

In Equations (41) and (42), the initial condition of V_(RC) _(_) _(a)[0]is set to be 0 (zero) because voltage at the RC circuit slowly changesaccording to the change of current even though the secondary batterycomes to an idle state or a no-load state and causes a current change atthe RC circuit.

In addition, the initial condition of z_(a)[0] is set to be identical toz_(cell)[0] because a state of the anode material is substantiallyidentical to the state of the secondary battery when the secondarybattery comes to an idle state or a no-load state.

Meanwhile, if the V_(RC) _(_) _(a)[0] is initialized as in Equation(41), the impedance voltage component V_(impedance) _(_) _(a)[k]included in the anode material circuit unit 210 may be initialized to R₀_(_) _(a)·i_(cell)[0]. However, if the secondary battery comes to ano-load state, i_(cell)[0] is 0 or near to 0. Therefore, the initialcondition V_(impedance) _(_) _(a)[0] may be regarded as being 0 or nearto 0.

Hereinafter, a method for the control unit 130 to estimate a voltage ofthe secondary battery whenever time Δt passes just after the secondarybattery comes to an idle state or a no-load state will be described indetail by using the voltage estimating model described above.

First, the control unit 130 initializes values of V_(RC) _(_) _(c2)[0],V_(RC) _(_) _(c2)[0], z_(c1)[0], and z_(c2)[0] corresponding to initialconditions of the cathode and values of V_(RC) _(_) _(a)[0] and z_(a)[0]corresponding to initial conditions of the anode by using the voltageV_(cell)[0] measured just after the secondary battery comes to an idlestate or a no-load state.V _(RC) _(_) _(c2)[0]=V _(RC) _(_) _(c2)[0]=V _(RC) _(_) _(a)[0]=0z _(c1)[0]=OCV ⁻¹ _(c1)(V _(cell)[0]+OCV _(a)(OCV _(cell) ⁻¹[0])))z _(c2)[0]=OCV ⁻¹ _(c2)(V _(cell)[0]+OCV _(a)(OCV _(cell) ⁻¹(V_(cell)[0])))z _(a)[0]=z _(cell)[0]=OCV ⁻¹ _(cell)(V _(cell)[0])

After that, the control unit 130 calculates i_(c1)[0] and i_(c2)[0] byapplying the initial conditions and the value of i_(cell)[0] toEquations (23) and (24) relating to the cathode. Here, if the secondarybattery comes to an idle state or a no-load state, value of i_(cell)[0]is substantially 0 or a constant having a small value near to 0.

$\begin{matrix}{{i_{c\; 1}\lbrack 0\rbrack} = {{\frac{\begin{matrix}{\left( {{{OCV}_{C\; 2}\left( {z_{C\; 2}\lbrack 0\rbrack} \right)} + {V_{{RC}_{C\; 2}}\lbrack 0\rbrack}} \right) -} \\{\left( {{{OCV}_{C\; 1}\left( {z_{C\; 1}\lbrack 0\rbrack} \right)} + {V_{{RC}_{C\; 1}}\lbrack 0\rbrack}} \right) -} \\{{i_{cell}\lbrack 0\rbrack}R_{0_{C\; 2}}}\end{matrix}}{R_{0_{C\; 1}} + R_{0_{C\; 2}}}****}*{i_{c\; 2}\lbrack 0\rbrack}}} \\{= \frac{\begin{matrix}{\left( {{{OCV}_{C\; 1}\left( {z_{C\; 1}\lbrack 0\rbrack} \right)} + {V_{{{RC}\_ C}\; 1}\lbrack 0\rbrack}} \right) -} \\{\left( {{{OCV}_{C\; 2}\left( {z_{C\; 2}\lbrack 0\rbrack} \right)} + {V_{{{RC}\_ C}\; 2}\lbrack 0\rbrack}} \right) -} \\{{i_{cell}\lbrack 0\rbrack}R_{0{\_ C}\; 1}}\end{matrix}}{R_{0{\_ C}\; 1} + R_{0{\_ C}\; 2}}}\end{matrix}$

If the i_(c1)[k] and i_(c2)[k] are calculated and time passes as much asΔt (k=1), the control unit calculates and obtains parameters requiredfor estimating V_(cathode)[1] and V_(anode)[1].

In other words, the control unit 130 obtains V_(RC) _(_) _(c1)[1],V_(RC) _(_) _(c2)[1], z_(c1)[1] and z_(c2)[1] by putting values ofV_(RC) _(_) _(c1)[0], V_(RC) _(_) _(c2)[0], i_(c1)[0] and i_(c2)[0] toEquations (27), (28), (29) and (30) with respect to the cathode, andobtains V_(RC) _(_) _(a)[1], z_(a)[1] by putting V_(RC) _(_) _(a)[0] andi_(cell)[0] to Equations (40) and (39) with respect to the anode,respectively.

${V_{{{RC}\_ c}\; 1}\lbrack 1\rbrack} = {{{V_{{{RC}\_ c}\; 1}\lbrack 0\rbrack}e^{- \frac{\Delta\; t}{R_{C\; 1}C_{C\; 1}}}} + {{R_{c\; 1}\left( {1 - e^{- \frac{\Delta\; t}{R_{C\; 1}C_{C\; 1}}}} \right)}{i_{c\; 1}\lbrack 0\rbrack}}}$${V_{{{RC}\_ c}\; 2}\lbrack 1\rbrack} = {{{V_{{{RC}\_ c}\; 2}\lbrack 0\rbrack}e^{- \frac{\Delta\; t}{R_{C\; 2}C_{C\; 2}}}} + {{R_{c\; 2}\left( {1 - e^{- \frac{\Delta\; t}{R_{C\; 2}C_{C\; 2}}}} \right)}{i_{c\; 2}\lbrack 0\rbrack}}}$z_(c 1)[1] = z_(c 1)[0] + i_(c 1)[0]Δ t/Q_(c 1)z_(c 2)[1] = z_(c 2)[0] + i_(c 2)[0]Δ t/Q_(c 1)${V_{{RC}\_ a}\lbrack 1\rbrack} = {{{V_{{RC}\_ a}\lbrack 0\rbrack}e^{- \frac{\Delta\; t}{R_{a}C_{a}}}} + {{R_{a}\left( {1 - e^{- \frac{\Delta\; t}{R_{a}C_{a}}}} \right)}{i_{cell}\lbrack 0\rbrack}}}$z_(a)[1] = z_(a)[0] − i_(cell)[0]Δ t/Q_(a)

After that, the control unit 130 calculates V_(cathode)[1], i_(c1)[1]and i_(c2)[1] by inputting the obtained parameters and i_(cell)[1]measured when Δt passes to Equations (22), (23) and (24) relating to thecathode. In addition, the control unit 130 calculates V_(anode)[1]inputting the obtained parameters and i_(cell)[1] to Equation (38)relating to the anode. If the calculation is completed, the control unit130 may estimate a voltage V_(cell)[1] of the secondary battery when Δtpasses once (namely, k=1) by subtracting V_(anode)[1] fromV_(cathode)[1].

${V_{cathode}\lbrack 1\rbrack} = {{\left( \frac{R_{0_{C\; 1}}R_{0_{C\; 2}}}{R_{0_{C\; 1}} + R_{0_{C\; 2}}} \right){\begin{pmatrix}\begin{matrix}{\frac{\left. {{{OCV}_{C\; 1}\left( {z_{c\; 1}\lbrack 1\rbrack} \right)} + {V_{{RC}_{C\; 1}}\lbrack 1\rbrack}} \right)}{R_{0_{C\; 1}}} +} \\{\frac{\left. {{{OCV}_{C\; 2}\left( {z_{c\; 2}\lbrack 1\rbrack} \right)} + {V_{{RC}_{C\; 2}}\lbrack 1\rbrack}} \right)}{R_{0_{C\; 2}}} -}\end{matrix} \\{i_{cell}\lbrack 1\rbrack}\end{pmatrix}****\mspace{20mu}{i_{c\; 1}\lbrack 1\rbrack}}} = \frac{\begin{matrix}{\left( {{{OCV}_{C\; 2}\left( {z_{c\; 2}\lbrack 1\rbrack} \right)} + {V_{{{RC}\_ C}\; 2}\lbrack 1\rbrack}} \right) -} \\{\left( {{{OCV}_{C\; 1}\left( {z_{c\; 1}\lbrack 1\rbrack} \right)} + {V_{{{RC}\_ C}\; 1}\lbrack 1\rbrack}} \right) -} \\{{i_{cell}\lbrack 1\rbrack}R_{0{\_ C}\; 2}}\end{matrix}}{R_{0{\_ C1}} + R_{0{\_ C}\; 2}}}$$\mspace{20mu}{{i_{c\; 2}\lbrack 1\rbrack} = \frac{\begin{matrix}{\left( {{{OCV}_{C\; 1}\left( {z_{c\; 1}\lbrack 1\rbrack} \right)} + {V_{{{RC}\_ C}\; 1}\lbrack 1\rbrack}} \right) -} \\{\left( {{{OCV}_{C\; 2}\left( {z_{c\; 2}\lbrack 1\rbrack} \right)} + {V_{{{RC}\_ C}\; 2}\lbrack 1\rbrack}} \right) -} \\{{i_{cell}\lbrack 1\rbrack}R_{0{\_ C}\; 1}}\end{matrix}}{R_{0{\_ C1}} + R_{0{\_ C}\; 2}}}$  V_(anode)[1] = OCV_(a)(z_(a)[1]) + V_(RC_a)[1] − i_(cell)[1]R_(0_a)  V_(cell)[1] = V_(cathode)[1] − V_(anode)[1]

The control unit 130 estimates V_(cathode)[k] by updating V_(RC) _(_)_(c1)[k], V_(RC) _(_) _(c2)[k], z_(c1)[k] and z_(c2)[k] with respect tothe cathode whenever Δt passes and estimates V_(anode)[k] by updatingV_(RC) _(_) _(a)[k] and z_(a)[k] with respect to the anode,substantially identical to the above. In addition, the control unit 130repeats the operation for estimating V_(cathode)[k] and V_(anode)[k]until the time index k reaches a preset number after the secondarybattery comes to an idle state or a no-load state. Therefore, thecontrol unit 130 may obtain an estimated voltage profile of thesecondary battery according to time during a preset measurement time.

Meanwhile, in the voltage estimating model described above, the pointwhen the time index k becomes 0 is not limited to a point just beforeand after the secondary battery comes to an idle state or a no-loadstate. Therefore, in a broad sense, V_(cell)[0] should be interpreted asa voltage measured for setting an initial condition when estimating avoltage of the secondary battery by using the voltage estimating model,regardless of the fact that the secondary battery is being discharged ordischarging is stopped when measuring the voltage, as obvious to thoseskilled in the art.

FIG. 12 shows an example of a voltage profile estimated by the controlunit 130, when a secondary battery including a blended cathode materialwhere an NMC cathode material and an LFP cathode material are mixed at aratio of 7:3 (weight ratio) comes to a no-load state while beingpulse-discharged in 5 c discharge current for 10 seconds in theintrinsic voltage range where voltage relaxation occurs.

In FIG. 12, a dotted line and a solid line represent voltage profilesrespectively estimated in a pulse discharge area and in a no-load statearea by using the voltage estimating model described above. Whenapplying the voltage estimating model, initial conditions required forcalculating V_(cathode)[k] and V_(anode)[k] are set by using V_(cell)[0]measured when initiating the pulse discharge. In addition, i_(cell)[k]is a pulse current value before the no-load state and is set to be 0after coming to the no-load state. In addition, Δt is set to be 1second.

Referring to FIG. 12, the voltage profile of the no-load state areaincludes an inflection point which supports the occurrence of voltagerelaxation in the secondary battery. In addition, it may be found that avoltage change pattern exhibited on the voltage profile is similar to avoltage change pattern exhibited when voltage relaxation occurs. Thisresult supports that, when the secondary battery including the blendedcathode material comes to an idle state or a no-load state in theintrinsic voltage range, the voltage estimating model according to thepresent disclosure may be usefully utilized to estimate a voltage changeof the secondary battery.

Meanwhile, if the secondary battery including the blended cathodematerial comes to an idle state or a no-load state while beingdischarged in the intrinsic voltage range, operating ions aretransferred between the first and second cathode materials included inthe blended cathode material to generate a voltage relaxationphenomenon. Therefore, in the case the secondary battery comes to anidle state or a no-load state in the intrinsic voltage range, it isneeded to add a resistance component R₀ _(_) _(relax) to the circuitmodel described above in order to model a current flow generated duringthe voltage relaxation. If the resistance component R₀ _(_) _(relax) isnot added, the inflection point supporting the occurrence of voltagerelaxation on the voltage profile estimated by the voltage estimatingmodel appears earlier than the actual appearance time. This will bedescribed later with reference to FIG. 16.

FIGS. 13 to 15 are circuit diagrams exemplarily showing variousconnection methods of the resistance component R₀ _(_) _(relax) in acircuit model for deriving the voltage estimating model.

Referring to FIG. 13, the resistance component R₀ _(_) _(relax) may beconnected in series between the first and second cathode materialscircuit units 221, 222. At this time, the resistance component R₀ _(_)_(relax) may be included in the circuit model as a separate resistancecomponent from the resistance components R₀ _(_) _(c1) and R₀ _(_)_(c2), included in the first and second cathode materials circuit units221, 222.

Referring to FIG. 14, the resistance component R₀ _(_) _(relax) may beconnected in series between the first and second cathode materialscircuit units 221, 222 and may be included in the circuit model as aresistance component comprising both the resistance components R₀ _(_)_(c1) and R₀ _(_) _(c2) included in the first and second cathodematerials circuit units 221, 222.

Referring to FIG. 15, in the case the first and second cathode materialscircuit units 221, 222 do not include an RC circuit, the resistancecomponent R₀ _(_) _(relax) may be connected in series between theopen-circuit voltage components of the first and second cathodematerials circuit units 221, 222.

Meanwhile, the connection method of the resistance component R₀ _(_)_(relax) is not limited to the above. Therefore, if the kind of theblended cathode material included in the secondary battery or theconfiguration of the circuit model changes, the connection method of theresistance component R₀ _(_) _(relax) may also be changed, as obvious tothose skilled in the art.

FIG. 16 is a comparative experiment result showing that the accuracy ofthe voltage estimating model is improved when the resistance componentR₀ _(_) _(relax) is added to the circuit model.

In FIG. 16, three voltage profiles I, II and III are depicted. Thevoltage profile I is a voltage profile exemplarily shown in FIG. 12, thevoltage profile II is a measured voltage profile of the secondarybattery, and the voltage profile III is a voltage profile estimated byusing the voltage estimating model derived from a circuit model havingthe resistance component R₀ _(_) _(relax).

Since the resistance component R₀ _(_) _(relax) is a resistancecomponent connected in series between the first and second cathodematerials circuit units 221, 222, in the equations of the voltageestimating model, if the size of R₀ _(_) _(c1) and/or R₀ _(_) _(c2)increases in proportion to the resistance component R₀ _(_) _(relax),the effects obtained by the addition of the resistance component R₀ _(_)_(relax) may be instantly reflected on various equations according tothe present disclosure. Therefore, the equations used for obtaining thevoltage profile I are used as they are when estimating the voltageprofile III, but only the magnitudes of R₀ _(_) _(c1) and R₀ _(_) _(c2)are suitably increased corresponding to the size of the resistancecomponent R₀ _(_) _(relax) In addition, if voltage relaxation occurs,the resistance of the first cathode material rapidly increases.Therefore, when reflecting R₀ _(_) _(relax) on R₀ _(_) _(c1) and/or R₀_(_) _(c2), the increase of R₀ _(_) _(c1) included in the first cathodematerial circuit unit 221 is set to be greater than the increase of R₀_(_) _(c2). In addition, the increase conditions of R₀ _(_) _(c1) and/orR₀ _(_) _(c2) applied when estimating the voltage profile III aredetermined by means of trial and error so as to minimize estimationerror of the voltage profile III.

Referring to FIG. 16, it may be found that the voltage profile I is notmatched with the voltage profile II but the voltage profile III is verysimilarly matched with the voltage profile II. This result supports thatthe accuracy of the voltage estimating model may be improved by addingthe resistance component R₀ _(_) _(relax) to the circuit model in orderto consider the voltage relaxation phenomenon induced when the secondarybattery comes to an idle state or a no-load state in the intrinsicvoltage range.

FIG. 17 shows that the voltage profile estimated by the voltageestimating model may be easily matched with an actual voltage profile ofthe secondary battery even though a voltage relaxation phenomenon isgenerated at different states or discharge conditions of the secondarybattery, if the magnitude of the resistance component R₀ _(_) _(relax)is adjusted so as to minimize the estimation error of the voltageprofile.

Graphs (a) to (d) shown in FIG. 17 are obtained by applying thefollowing conditions.

graph (a): the secondary battery comes to the no-load state while beingpulse-discharged in 2 c-rate under the condition that a state of thesecondary battery is 0.25 before the pulse-discharging.

graph (b): the secondary battery comes to the no-load state while beingpulse-discharged in 5 c-rate under the condition that a state of thesecondary battery is 0.30 before the pulse-discharging.

graph (c): the secondary battery comes to the no-load state while beingpulse-discharged in 5 c-rate under the condition that a state of thesecondary battery is 0.20 before the pulse-discharging.

graph (d): the secondary battery comes to the no-load state while beingpulse-discharged in 2 c-rate under the condition that a state of thesecondary battery is 0.20 before the pulse-discharging.

In the graphs (a) to (d), dotted lines correspond to estimated voltageprofiles of the secondary battery obtained by using the voltageestimating model, and solid lines correspond to measured voltageprofiles of the secondary battery.

When obtaining a profile depicted with a dotted line by using thevoltage estimating model, the size of R₀ _(_) _(relax) is adjusted byincreasing R₀ _(_) _(c1) and/or R₀ _(_) _(c2). In addition, the increaseconditions of R₀ _(_) _(c1) and/or R₀ _(_) _(c2) are determined by meansof trial and error.

The graphs (a) to (d) shows that an estimated voltage profile of thesecondary battery may be easily matched with a measured profile if themagnitude of R₀ _(_) _(relax) is suitably adjusted, even though a stateor a discharge condition of the secondary battery changes and so theappearance time (see τ_(relax)) of the inflection point supporting theoccurrence of voltage relaxation and the voltage change pattern arechanged differently. Therefore, it may be understood that R₀ _(_)_(relax) is one of important factors determining the accuracy of thevoltage estimating model in the intrinsic voltage range where voltagerelaxation occurs.

Meanwhile, as described above with reference to Equation (7), based on atime point just after the secondary battery comes to an idle state or ano-load state (namely, k=0) in the intrinsic voltage range, R₀ _(_)_(relax) is proportional to a capacity (1−z_(c2)[0]) of operating ionsintercalated into the second cathode material and inversely proportionalto a residual capacity (z_(c1)[0]) of the first cathode material capableof receiving operating ions.

Therefore, R₀ _(_) _(relax) may be expressed like Equation (44) below asa function of a parameter X_(relax) which may be expressed by Equation(43) below.

$\begin{matrix}{X_{relax} = \frac{\left( {1 - {z_{C\; 2}\lbrack 0\rbrack}} \right)Q_{C\; 1}}{{z_{C\; 1}\lbrack 0\rbrack}Q_{C\; 2}}} & (43) \\{R_{0{\_{relax}}} = {H\left( X_{relax} \right)}} & (44)\end{matrix}$

Assuming that a function using the X_(relax) as an input parameter is H,an embodiment of the function H may be obtained through an experimentbelow.

First, a measured voltage profile M_(i) of the secondary battery isobtained for each of a plurality of SOC, conditions which cause voltagerelaxation. After that, an estimated profile E_(i) capable of being mostclosely matched with the measured profile M_(i) is identified by meansof trial and error while variously changing the initial conditionsz_(c1)[0] and z_(c2)[0] and the resistance component R₀ _(_) _(relax) ofthe voltage estimating model. After that, z _(c1)[0]_(i), z_(c2)[0]_(i), and R ₀ _(_) _(relax,i) used for obtaining the identifiedestimated profile E_(i) are determined. Here, the symbol ‘-’ and thesubscript ‘i’ affixed to the letters of the state parameter z and theresistance parameter R represent that each parameter is an optimalparameter used for obtaining the estimated profile E_(i). If z_(c1)[0]_(i), z _(c2)[0]_(i), and R ₀ _(_) _(relax,i) are identified asdescribed above, data set (X_(relax), R₀ _(_) _(relax))_(i) may beobtained for each SOC_(i) by using Equation (43). If a number of SOC_(i)sampled in the intrinsic voltage range is n, data sets (X_(relax), R₀_(_) _(relax))_(i) [k=1, 2, 3, . . . , n−1, n] may be obtained and thefunction H may be obtained by numerically analyzing the data sets.

FIG. 18 is a graph showing a changing pattern of an H function, afterobtaining the H function with respect to a secondary battery including ablended cathode material where an NMC cathode material and an LFPcathode material are mixed at a ratio of 7:3 (weight ratio). The Hfunction shown in FIG. 18 is a polynomial function which may beexpressed like Equation (45) below.R ₀ _(_) _(relax) =aX _(relax) ³ +bX _(relax) ² +cX _(relax) ¹ +d  (45)

Constants a, b, c and d of the polynomial function may be specified bynumerically analyzing data sets (X_(relax), R₀ _(_) _(relax))_(i) [k=1,2, 3, . . . , n−1, n] and may be changed as desired according to thekind of the blended cathode material included in the secondary batteryand the circuit model used for deriving the voltage estimating model. Inaddition, since the H function may be expressed in a way different fromthe polynomial function according to the numerical analysis method, thepresent disclosure is not limited to a specific example of the Hfunction. In addition, since the data sets (X_(relax), R₀ _(_)_(relax))_(i) [k=1, 2, 3, . . . , n−1, n] may be made in a form of alook-up table, the H function should be interpreted as including thelook-up table, as obvious to those skilled in the art.

Referring to FIG. 18, it may be understood that X_(relax) and R₀ _(_)_(relax) have the same changing tendency. In other words, if X_(relax)increases, R₀ _(_) _(relax) also increases, or vice versa. This supportsonce more that the parameter R₀ _(_) _(relax) is proportional to acapacity (1−z_(c2)[0]) of operating ions intercalated into the secondcathode material and inversely proportional to a residual capacity(z_(c1)[0]) of the first cathode material capable of receiving operatingions when the secondary battery comes to an idle state or a no-loadstate.

Hereinafter, a method for the secondary battery managing apparatus toestimate a state of a secondary battery in the intrinsic voltage rangeby using a voltage estimating model on which the resistance component R₀_(_) _(relax) is reflected will be described in detail.

FIGS. 19 and 20 are flowcharts for illustrating a process for thesecondary battery managing apparatus to estimate a state of a secondarybattery.

Referring to FIGS. 19 and 20 together with FIG. 10, the process ofestimating a state of the secondary battery 110 is performed by thesensor 120, the control unit 130 and the storage unit 160 included inthe secondary battery managing apparatus.

First, if the secondary battery 110 starts being discharged, the controlunit 130 determines whether Δt_(monitor) has passed (S10). Here, theΔt_(monitor) represents a time interval in which the control unit 130monitors an electric characteristic of the secondary battery 110 whenthe secondary battery is being discharged. If it is determined thatΔt_(monitor) has passed, the control unit 130 receives an electriccharacteristic of the secondary battery 110, measured by the sensor 120,from the sensor 120 and stores the electric characteristic in thestorage unit 160 together with time stamps (S20). Here, the electriccharacteristic includes at least voltage V_(cell) and discharge currenti_(cell) of the secondary battery. In addition, the time stamp meanstime when the control unit 130 receives the electric characteristic fromthe sensor 120 or time when data relating to the electric characteristicis stored in the storage unit 160. This concept will be identically usedbelow.

After Step S20, the control unit 130 determines whether the secondarybattery 110 comes to an idle state or a no-load state, by using theelectric characteristic stored in the storage unit 160 (S30). Thisdetermination may be made by using the magnitude of the dischargecurrent i_(cell) of the secondary battery. In other words, if themagnitude of the discharge current i_(cell) decreases substantially to 0or less than a preset size (for example, several mA), the secondarybattery 110 may be regarded as coming to an idle state or a no-loadstate. Here, when it is determined that the idle or no-load condition issatisfied, the voltage and the discharge current of the secondarybattery 110 stored in the storage unit 160 are respectively designatedas an initial voltage and an initial current. If it is determined thatthe idle or no-load condition is not satisfied, the control unit 130returns the process to Step S10 and then repeats the process ofreceiving an electric characteristic from the sensor 120 whenΔt_(monitor) passes and storing the electric characteristic in thestorage unit 160. Therefore, if the idle or no-load condition is notsatisfied, whenever Δt_(monitor) passes, the control unit 130 repeatsthe process of receiving an electric characteristic of the secondarybattery 110 from the sensor 120 and storing the electric characteristicin the storage unit 160 together with a time stamp.

Meanwhile, if it is determined that the idle or no-load condition issatisfied, the control unit 130 executes the next step to initialize atime index k used at the voltage estimating model to 0 (S40). Afterthat, the control unit 130 allocates the initial voltage and the initialcurrent to V_(cell)[0] and i_(cell)[0] and stores the same in thestorage unit 160 together with a time stamp (S50).

Subsequently, the control unit 130 determines whether Δt has passed.Here, the Δt represents a time interval in which the control unit 130monitors an electric characteristic of the secondary battery 110 afterthe secondary battery 110 comes to an idle state or a no-load state. Ifit is determined that Δt has passed, the control unit 130 increases thetime index k as much as 1 (S70). After that, the control unit 130receives the electric characteristic of the secondary battery 110,measured by the sensor 120, from the sensor 120, allocates the voltageand current of the secondary battery respectively to V_(cell)[k] andi_(cell)[k] (at the present, k is 1), and then stores the same in thestorage unit 160 together with a time stamp (S80).

After that, the control unit 130 determines whether the presetmeasurement time has passed (S90). In addition, if it is determined thatthe measurement time has not passed, the control unit 130 returns theprocess to Step S60 and then repeat the processes of increasing the timeindex k, receiving the electric characteristic from the sensor 120,allocating the voltage and current of the secondary battery 110 toV_(cell)[k] and i_(cell)[k], and storing the same in the storage unit160 together with a time stamp, whenever Δt passes. Therefore, aplurality of data sets of V_(cell)[k] and i_(cell)[k] are stored in thestorage unit 160 together with time stamps before the measurement timepasses. Here, a plurality of V_(cell)[k] and time stamps constitute avoltage profile of the secondary battery. Likewise, a plurality ofi_(cell)[k] and time stamp constitute a current profile of the secondarybattery.

Meanwhile, if it is determined that the preset measurement time haspassed in Step S90, the control unit 130 performs the next step to readthe measured voltage profile from the storage unit 160 (S100). Here,reading the voltage profile means that a plurality of V_(cell)[k] andtime stamps are read out from the storage unit 160 by the control unit130. After that, the control unit 130 analyzes the voltage profile todetermine whether the voltage relaxation occurrence condition describedabove may be satisfied (S110).

If the voltage relaxation occurrence condition is satisfied, the controlunit 130 estimates a state of the secondary battery by using the voltageestimating model described above (S120).

In an embodiment, the control unit 130 may estimate a state of thesecondary battery by means of iteration. Here, the term ‘iteration’means a method for estimating a state of the secondary battery, in whicha plurality of estimated voltage profiles of the secondary battery areobtained while changing parameters z_(c1)[0] and z_(c2)[0] of theinitial condition of the voltage estimating model according to thepresent disclosure and a parameter R₀ _(_) _(relax) which should beadded to the circuit model when voltage relaxation occurs, an estimatedprofile most closely matched with the voltage profile read in Step S100is identified from the plurality of obtained estimated profiles, andinitial conditions z*_(c1)[0] and z*_(c2)[0] used for obtaining theidentified estimated profile are used to estimate a state of thesecondary battery by using Equation (46) below.z _(cell) =z* _(c1)[0]Q* _(c1) +z* _(c2)[0]Q* _(c2)  (46)

FIG. 21 is a flowchart for illustrating a process of estimating a stateof the secondary battery by means of iteration according to anembodiment of the present disclosure in more detail.

First, if the process for estimating a state of the secondary batterystarts, the control unit 130 initializes an iteration index p to 1(S121). After that, the control unit 130 allocates initial values α₁ andβ₁ to parameters z_(c1)[0] and z_(c2)[0] relating to an amount ofoperating ions having reacted with the first and second cathodematerials, among the initial conditions used for obtaining estimatedvoltage profiles of the secondary battery by using the voltageestimating model (S122). Subscripts affixed to α and β representiteration indexes.

The α₁ and β₁ may be set arbitrarily. However, considering that thevoltage relaxation phenomenon occurs in an early stage when a capacityof the first cathode material capable of reacting with operating ions issignificantly used and the second cathode material starts reacting withoperating ions, a value very close to 1, for example 0.98, is set to β₁.In addition, when defining that the state of the secondary battery justbefore coming to an idle state or a no-load state is z_(cell) _(_)_(discharge), the control unit 130 may calculate z_(cell) _(_)_(discharge) by integrating discharge current by means of amperecounting from the time when the secondary battery 110 starts beingdischarged and may maintain the value in the storage unit 160. Inaddition, z_(cell) to be estimated by the control unit 130 has a valuenear to z_(cell) _(_) _(discharge). Therefore, α₁ is preferably set tobe slightly higher or lower than a value which may be obtained as asolution when inputting preset β₁ and z_(cell) _(_) _(discharge) toEquation (46) respectively as z*_(c2)[0] and z_(cell). If α₁ is set tobe greater than the solution and then a value allocated to z_(c1)[0] isgradually decreased from the next iteration period or if α₁ is set to belower than the solution and then a value allocated to z_(c1)[0] isgradually increased from the next iteration period, the estimatedvoltage profile of the secondary battery calculated by the voltageestimating model becomes closer to an actually measured voltage profile,and so an approximate estimated profile capable of being matched withthe measured voltage profile may be easily identified.

After allocating initial values to z_(c1)[0] and z_(c2)[0], the controlunit 130 sets the initial condition of the voltage estimating model asfollows (S123). The method of deriving an initial condition of thevoltage estimating model has been described above, and not described indetail here.V _(RC) _(_) _(c2)[0]=V _(RC) _(_) _(c2)[0]=V _(RC) _(_) _(a)[0]=0z _(c1)[0]=α₁z _(c2)[0]=β₁z _(a)[0]=z _(cell)[0]=α₁ Q* _(c1)+β₁ Q* _(c2)

In order to reflect a resistance component R₀ _(_) _(relax) appearingwhen voltage relaxation occurs on the voltage estimating model, thecontrol unit 130 calculates X_(relax,p=1) according to Equation (47)below, and quantitatively calculates R₀ _(_) _(relax,p=1) by Equation(48) below (S124).

$\begin{matrix}{X_{{relax},{p = 1}} = \frac{\left( {1 - \beta_{1}} \right)Q_{C\; 1}}{\alpha_{1}Q_{C\; 2}}} & (47) \\{R_{0_{relax},{p = 1}} = {H\left( X_{relax} \right)}} & (48)\end{matrix}$

Subsequently, the control unit 130 reflects the resistance component,exhibited when voltage relaxation occurs by increasing the size ofresistance component R₀ _(_) _(c1) and/or R₀ _(_) _(c2), among theparameters included in the equations of the voltage estimating modelaccording to the size of R₀ _(_) _(relax,p=1), on the voltage estimatingmodel (S125). The method of reflecting the resistance component on thevoltage estimating model has been described above and is not describedin detail here.

After that, the control unit 130 calculates an estimated voltage profileof the secondary battery by estimating the voltage V_(cell)[k] of thesecondary battery whenever Δt passes while increasing the time index kas much as 1 during a predetermined estimation time by using theequations of the voltage estimating model where R₀ _(_) _(relax,p=1) isreflected and the initial condition set in S123, and stores theestimated voltage profile in the storage unit 160 (S126). Here, theestimation time and Δt parameters may be set to be substantiallyidentical to the measurement time and Δt which are parameters used forobtaining a measured voltage profile of the secondary battery. Inaddition, the method of calculating the estimated profile whileincreasing the time index k has been described above and is notdescribed in detail here.

After that, the control unit 130 calculates an error present between themeasured voltage profile of the secondary battery obtained through StepsS50 to S80 and the estimated voltage profile of the secondary batteryobtained in Step S126 (S127). The error may be calculated by using, forexample, a root mean square of differences between the measured voltageprofile and the estimated voltage profile.

Subsequently, the control unit 130 determines whether an error varianceis lower than a critical value (S128). At the present, since theiteration index p is 1, it is impossible to calculate the errorvariance. Therefore, the error variance is calculated from the pointthat the iteration index p is 2.

The critical value is set to be a value near to 0. If the error variancedecreases lower than the critical value near to 0, this means that anestimated voltage profile of the secondary battery most closely matchedwith the measured voltage profile is obtained. In other words, an errorpresent between the estimated voltage profile of the secondary batteryand the measured voltage profile converges towards a minimal value.

If it is determined that the error variance is not lower than thecritical value, the control unit 130 increases the iteration index p asmuch as 1 (S129). After that, the control unit 130 executes Step S122 toallocate initial values α₂ and β₂ to the parameters z_(c1)[0] andz_(c2)[0] again (S122). Subscripts affixed to α and β representiteration indexes.

Here, the values of α₂ and β₂ may be set based on the values of α₁ andβ₁. In an embodiment, the value of β₂ may be fixed to the value of β₁,and the value of α₂ may be decreased by a predetermined value based onα₁. For example, if α₁ and β₁ are respectively 0.30 and 0.98, values ofα₂ and β₂ may be respectively set to be 0.295 and 0.98.

The method of setting the values of α₂ and β₂ is not limited to theabove. In other words, changing breadth and changing direction of α₂ andβ₂ based on α₁ and β₁ may be modified in various ways. In a modifiedembodiment, the values of α₂ and β₂ may be increased or decreased by acertain value from the values of α₁ and β₁. For example, if the valuesof α₁ and β₁ are respectively 0.30 and 0.98, the values of α₂ and β₂ maybe respectively set to be 0.295 and 0.981. In another modifiedembodiment, the value of α₂ may be fixed to the value of α₁, the valueof β₂ may be increased by a predetermined value from the value of β₁.For example, if the values of α₁ and β₁ are respectively 0.30 and 0.98,the values of α₂ and β₂ may be respectively set to be 0.30 and 0.981.

If setting the initial values α₂ and β₂ to z_(c1)[0] and z_(c2)[0], thecontrol unit 130 calculates the resistance component R₀ _(_)_(relax,p=2) in Step S124 by using the method described above, reflectsR₀ _(_) _(relax,p=2) on the voltage estimating model in Step S125,obtains an estimated voltage profile of the secondary battery in S126 byusing the voltage estimating model where R₀ _(_) _(relax,p=2) isreflected, calculates an error between the estimated voltage profile ofthe secondary battery and the measured voltage profile in Step S127,determines whether the error variance is lower than the critical valuein Step S128, increases the iteration index p as much as 1 in S129 ifthe error variance is not lower than the critical value, and performsthe next process loop in the same way as above so that the aboveprocedure is repeated. The error variance decreases as the process looprepeats, and if the iteration loop repeats sufficiently, the errorvariance decreases to a value near to 0 and eventually lower than thecritical value. If the error variance is close to 0, an error presentbetween the estimated voltage profile of the secondary battery and themeasured voltage profile becomes minimal, and an estimated voltageprofile of the secondary battery approximately matched with the measuredvoltage profile is obtained.

If it is determined that the error variance decreases lower than thecritical value, the control unit 130 considers the estimated profile atthis time as an approximate estimated profile most closely matched withthe measured voltage profile of the secondary battery, and estimates astate z_(cell) of the secondary battery according to Equation (49) belowby using α_(p)* and β_(p)* allocated to z_(c1)[0] and z_(c2)[0] whenobtaining the approximate estimated profile (S130). Here, the subscript‘p*’ represents that the values α and β are parameters used whenobtaining the approximate estimated voltage profile.z _(cell)=α_(p*) Q* _(c1)+β_(p*) Q* _(c2)  (49)

In an embodiment, if α_(p*) and β_(p*) are respectively 0.105 and 0.98and Q*_(c1) and Q*_(c2) are respectively 0.8 and 0.2, the state z_(cell)of the secondary battery becomes 0.28 (28%).

Meanwhile, the control unit 130 may also obtain an approximate estimatedprofile by using a modified method below, different from the above.

In other words, the control unit 130 may obtain corresponding R₀ _(_)_(relax,p) from a plurality of α_(p) and β_(p) values, obtain thecorresponding estimated voltage profiles of the secondary battery byusing a plurality of parameters α_(p), β_(p) and R₀ _(_) _(relax,p),identify an approximate estimated profile having a minimal error withthe measured voltage profile of the secondary battery from the pluralityof obtained estimated profiles, and calculate an estimated value of thestate of the secondary battery from the α_(p*) and β_(p*) values usedfor calculating the identified approximate estimated profile. At thistime, the method of changing α_(p) and β_(p) values may adopt themethods employed in the former embodiments, and preferably, values wherethe α₁, and/or β_(p) start and stop changing and the changing width aresuitably set so that an approximate estimated profile whose error isnear to 0 may be included in the plurality of the estimated profiles.

FIG. 22 is an experiment result showing that the state of a secondarybattery estimated according to the state estimating method as describedabove may be closely matched with an actual state of the secondarybattery.

In this experiment, a secondary battery including a cathode having ablended cathode material where an NFC cathode material and an LFPcathode material are blended at a ratio of 7:3 (weight ratio) and ananode having a carbonaceous anode material was used. The secondarybattery was charged until the state z_(cell) becomes 1. After that, thesecondary battery was discharged until the state of the secondarybattery becomes 0.30 where voltage relaxation may occur. The state of0.30 is calculated by means of the ampere-counting method. Subsequently,after the secondary battery was left alone for 24 hours, an open-circuitvoltage (OCV) was measured and an actual state of the secondary batterywas calculated with reference to an OCV-state look-up table. As aresult, the secondary battery was checked to have an actual state of0.333, which has an error of 0.033 (about 10%) from a state valuecalculated by means of the ampere-counting method. This error is atraditional problem of the ampere-counting method and is caused becausemeasurement errors generated when measuring a discharge current of thesecondary battery is accumulated while counting the discharge current.

After checking an actual state of the secondary battery as describedabove, 5 c pulse discharge was performed to the secondary battery for 10seconds and then stopped so that the secondary battery comes to ano-load state, and the no-load state was maintained after 100 secondspassed. When this no-load shifting experiment was being performed, avoltage of the secondary battery was measured for 100 seconds from thepoint that the pulse discharge was initiated. The measured voltages areshown as a voltage profile in (a) section of FIG. 22. Referring to thevoltage profile, the following features may be checked.

An inflection point supporting the occurrence of voltage relaxation islocated near 20 seconds.

Since the inflection point is present at the voltage profile, thesecondary battery may be regarded as coming to the no-load state in theintrinsic voltage range where voltage relaxation occurs.

Just after the secondary battery comes to the no-load state, voltagerapidly rises to 3.2V over several seconds, and two voltage rises aremade before and after the inflection point. In detail, after the rapidvoltage rise, a voltage variance of 250 mV during the two voltage risesis observed for about 20 seconds.

About 60 seconds are consumed until the voltage of the secondary batteryreaches an equilibrium voltage of about 3.5V.

If a state of the secondary battery is estimated from a OCV-statelook-up table while regarding the voltage measured when 30 seconds passafter the starting of the no-load state as an open-circuit voltage ofthe secondary battery, the estimated state value is 0.27. This statevalue has a great deviation from an actual state value. Therefore, thestate may not be exactly estimated if being calculated by using avoltage of the secondary battery measured at the no-load state, unlessthe secondary battery maintains the no-load state for a sufficient time.

In this experiment, a plurality of estimated voltage profiles of thesecondary battery were obtained by applying the voltage estimationmethod shown in FIGS. 19 and 20.

The section (b) of FIG. 22 is a graph showing estimated voltage profilesof the secondary battery, calculated while increasing the iterationindex p by 1, together with an actually measured voltage profile. Inaddition, the section (c) of FIG. 22 shows the change of an estimatedstate of the secondary battery corresponding to each estimated profileaccording to the increase of the iteration index p, in comparison to theactual state (0.333) of the secondary battery.

As shown in FIG. 22, it may be found that the estimated profilesgradually converge towards the measured voltage profile as the iterationindex p increases. In addition, it may also be found that the estimatedstate corresponding to each estimated profile converges towards theactual state as the iteration index (140 or above) increases. In thisexperiment, the estimated state converges towards 0.331, and theconverging value has an error of just 0.6% in comparison to the actualstate of 0.333. This experiment result shows that the present disclosuremay accurately estimate a state of a secondary battery substantially inthe same level as an actual state.

FIG. 23 shows another experiment result supporting the robustness of thestate estimating method according to the present disclosure. In thisexperiment, five actual states of the secondary battery different fromeach other are reliably measured by using an OCV-state look-up table asdescribed above. Thereafter, initial conditions α_(p*) and β_(p*) withrespect to each of the five actual states are determined by the methodas described above. Here, each of the initial conditions α_(p*) andβ_(p*) is capable of estimating a state to be matched with an actualstate. The five determined α_(p*) and β_(p*) values and the estimatedvoltage profiles of the secondary battery obtained by using the α_(p*)and β_(p*) values are shown in FIG. 23. In addition, an estimated SOCvalue, SOC_(estimate), calculated from each α_(p*) and β_(p*) by usingthe Equation (49), an actual SOC value, SOC_(real), and an error betweenthem are listed in Table 1 below.

TABLE 1 α_(p)* β_(p)* SOC_(estimate) SOC_(real) error 0.20 0.98 0.3560.356 0 0.15 0.98 0.316 0.316 0 0.10 0.98 0.276 0.276 0 0.07 0.98 0.2520.252 0 0.05 0.98 0.236 0.236 0

Referring to Table 1, it may be understood that the estimated statevalue of the secondary battery is closely matched with the actual statevalue. Therefore, when estimating a state of the secondary battery byusing the voltage estimating model described above, it may be understoodthat z_(c1)[0] and z_(c2)[0] corresponding to initial conditions areimportant parameters in determining a state of the secondary battery.

In addition, referring to FIG. 23, when β_(p*) is fixed to 0.98, it maybe understood that the point when an inflection point occurs in theestimated voltage profile of the secondary battery is delayed as α_(p*)decreases. This is because the resistance component R₀ _(_) _(relax)increases due to the decrease of α_(p*). When voltage relaxation occursbetween the first and second cathode materials, if a residual capacityof operating ions capable of being intercalated into the first cathodematerial to which operating ions are transferred decreases, theresistance component R₀ _(_) _(relax) increases, as described above.Therefore, the changing pattern of the estimated profiles shown in FIG.23 experimentally supports that the presumption of R₀ _(_) _(relax)being inversely proportional to z_(c1)[0] is reasonable.

Meanwhile, according to another embodiment, the control unit 130 mayestimate a state of the secondary battery by using a look-up tablepreviously stored in the storage unit 160, instead of the voltageestimating model to which iteration should be applied.

The look-up table may have a data structure which may refer to a stateSOC_(estimate) of the secondary battery by a reference parameter. Thereference parameter may be at least one parameter selected from thegroup consisting of a voltage V* of an inflection point occurring in thevoltage profile when the secondary battery comes to an idle state or ano-load state in the intrinsic voltage range, time T* taken until theoccurrence of the inflection point, a voltage variance amount ΔV*obtained by adding voltage changes during a Predetermined time periodbefore and after the inflection point and a first-order differentialvalue

$\left. \frac{d\; V}{d\; t} \right)_{t = T^{*}}$calculated at the inflection point.

In order to make the look-up table, a plurality of dischargingexperiments for the secondary battery is performed in differentdischarge currents while varying a state of the secondary battery in theintrinsic voltage range. In the experiments, voltage profiles includingan inflection point are obtained and then reference parameters V*, T*,ΔV*,

$\left. \frac{d\; V}{d\; t} \right)_{t = T^{*}}$of each voltage profile are calculated and stored in the look-up table.

The reference parameter is an element defining a shape of the voltageprofile including the inflection point. Therefore, the greater thenumber of reference parameters are, the shape of the voltage profile maybe defined more accurately. Therefore, if the number of referenceparameters used for estimating a state of the secondary batteryincreases, the state of the secondary battery may be estimated moreaccurately.

Meanwhile, any parameter capable of defining a shape of a voltageprofile including an inflection point may be considered as the referenceparameter without restriction. For example, a value obtained byintegrating a voltage profile between predetermined two points beforeand after the inflection point, or a first-order or a second-orderdifferential value of voltage profiles calculated at a predeterminedpoint before and/or after the inflection point may also be considered asa reference parameter. Therefore, it should be understood that thepresent disclosure is not limited to the specific kind or number ofreference parameters.

In case of estimating a state of the secondary battery by using thelook-up table, the control unit 130 reads the measured voltage profileof the secondary battery stored in the storage unit 160 in Step S100 ofFIG. 20, and then calculates at least one reference parameter from themeasured voltage profile. Here, the reference parameter includes atleast one selected from the group of V*, T*, ΔV* and

$\left. \frac{d\; V}{d\; t} \right)_{t = T^{*}}.$If the reference parameter is calculated, the control unit 130 estimatesa state of the secondary battery corresponding to the referenceparameter with reference to the look-up table.

In another embodiment of the present disclosure, correlations betweenthe reference parameters included in the look-up table and states of thesecondary battery may be converted into a look-up function. The look-upfunction means a function which uses at least one reference parameterand a state of the secondary battery corresponding thereto as an inputparameter and an out parameter, respectively.

In an embodiment, the look-up function may be expressed like Equation(50) below.

$\begin{matrix}\left. {{SOC}_{estimate} = {{Look\_ up}\left( {{{combination}\left\{ {V^{*},T^{*},{\Delta\; V^{*}},\frac{d\; V}{d\; t}} \right)_{t = T^{*}}},\ldots}\mspace{14mu} \right\}}} \right) & (50)\end{matrix}$

In Equation (50), an operator “combination{ }” within the equation (50)is a function which selects at least one of the reference parameters asan input parameter of “Look_up function”, and “Look_up function” is afunction which outputs a state of the secondary battery corresponding tothe reference parameters selected by the operator “combination{ }”. The“Look_up function” may be defined differently according to the kind andnumber of input parameter(s) selected by the operator “combination{ }”and may be derived by numerical analysis of data included in the look-uptable. For example, assuming V* and T* as input parameters andSOC_(estimate,n) as an output parameter, if a plurality of data sets forV*, T*, SOC_(estimate) are numerically analyzed, “Look_up function”capable of calculating SOC_(estimate) from V* and T* may be derived.

In case of estimating a state of the secondary battery by using thelook-up function, the control unit 130 reads the measured voltageprofile of the secondary battery stored in the storage unit 160 in StepS100 of FIG. 20, and then calculates at least one reference parameterfrom the measured voltage profile. Here, the reference parameter mayinclude at least one selected from the group of V*, T*, ΔV* and

$\left. \frac{d\; V}{d\; t} \right)_{t = T^{*}}.$After that, the control unit 130 may obtain a state of the secondarybattery as an output value by inputting the reference parameter to thelook-up function.

If the control unit 130 estimates a state of the secondary battery byusing the look-up table or the look-up function, the state of thesecondary battery may be accurately estimated in a simple way incomparison to the case where the voltage estimating model is used.

According to another embodiment of the present disclosure, the controlunit 130 may analyze a changing pattern of the voltage measured by thesensor 120 in real time by calculating an inflection point parameterwhenever the voltage is measured, and then, if the calculated inflectionpoint parameter corresponds to a condition under which voltagerelaxation is detected, the control unit may estimate a state of thesecondary battery by using the calculated inflection point parameter atthat time, a voltage measured when the condition under which voltagerelaxation is detected is established, a time when the voltage ismeasured, or the like.

For example, whenever a voltage is measured by the sensor 120, thecontrol unit 130 may receive the voltage value from the sensor 120 andcalculate a first-order differential value or a second-orderdifferential value of the voltage value with respect to the measurementtime as an inflection point parameter, and then, if a condition underwhich the first-order differential value becomes maximum or thesecond-order differential value becomes zero is established, the controlunit may determine the maximum value of the first-order differentialvalue and/or the time taken until the condition is established and/or avoltage when the condition is established as a reference parameter andestimate a state of the secondary battery by using a look-up table or alook-up function defining the relations between a state of the secondarybattery and a reference parameter regarding the inflection point inadvance. Of course, the look-up table and the look-up function may beobtained by experiments as described above.

Here, the inflection point parameter represents a parameter by which aninflection point may be identified in real time in the changing patternof a voltage, and the above descriptions are just examples. Therefore,any parameter by which an inflection point occurring in the changingpattern of the voltage measured by the sensor 120 may be identified inreal time may be determined as the inflection point parameter.

Meanwhile, in another embodiment of the present disclosure, the controlunit 130 may update the state of the secondary battery, estimated beforethe secondary battery comes to an idle state or a no-load state andstored in the storage unit 160, to the state of the secondary batteryestimated according to the method of the present disclosure. Thisprocess may be selectively added as Step S140 after Step S120 of FIG.20. Step S140 is depicted with a dotted line because this step isoptional.

As described above, the ampere-counting method widely used forestimating a state of a secondary battery has a measurement error andthe error increases as time passes. This problem is not limited to theampere-counting method, and other kinds of methods for stating a stateof a secondary battery known in the art also have similar problems.Therefore, when a secondary battery comes to an idle state or a no-loadstate in an intrinsic voltage range, the state of the secondary batterymay be corrected to a more accurate value by accurately estimating astate of the secondary battery according to the present disclosure andthen updating a state value estimated before the secondary battery comesto the idle state or the no-load state to the accurately estimated statevalue. For example, if an electric vehicle driven by a secondary batterytemporarily stops at a traffic signal, which results in the secondarybattery shifting to an idle state or a no-load state, a state of thesecondary battery may be estimated according to the present disclosure,and a state of the secondary battery estimated by using anampere-counting method may be updated to the newly estimated state.

In another embodiment of the present disclosure, the control unit 130may be electrically connected to the display unit 150, and the state ofthe secondary battery estimated at the idle state or the no-load statemay be displayed through the display unit 150, for example as a graphicinterface. This process may be selectively added as Step S150 after StepS120 of FIG. 20. Step S150 is depicted with a dotted line because thisstep is optional.

The display unit 150 may not be included in the secondary batterymanaging apparatus according to the present disclosure and alternativelymay be included in another device connected to the secondary batterymanaging apparatus. In the latter case, the display unit 150 and thecontrol unit 130 are not directly connected but indirectly connected tothe display unit via a control unit included in another device.Therefore, the electric connection between the display unit 150 and thecontrol unit 130 should be understood as including such an indirectconnection.

Meanwhile, if the state of the secondary battery estimated by thecontrol unit 130 according to the present disclosure may not be directlydisplayed through the display unit 150, the state value may be providedto another device including the display unit 150. In this case, thecontrol unit 130 may be connected to another device for allowing datatransmission, and another device may receive the state of the secondarybattery from the control unit 130 and display the received state valueas a graphic interface through the display unit 150 connected thereto.

The graphic interface is not specially limited if it may display thestate of the secondary battery to the user. FIG. 24 shows variousexamples of the graphic interface.

As shown in FIG. 24, the graphic interface may adopt (a) displaying thestate of the secondary battery with the length of a bar graph, (b)displaying the state of the secondary battery with gauge pointers, (c)displaying the state of the secondary battery with numerals, or thelike.

Meanwhile, any combinations of various control logics of the controlunit 130 may become embodiments of the secondary battery managing methodof the present disclosure. Therefore, the secondary battery managingmethod will not be described in detail here.

In addition, any combinations of various control logics of the controlunit 130 may be composed in computer-readable program codes and recordedin a computer-readable recording medium. The recording medium is notspecially limited if it may be accessed by a processor included in acomputer. For example, the recording medium includes at least oneselected from the group consisting of ROM, RAM, register, CD-ROM,magnetic tape, hard disk, floppy disk and optical data storage. Thecomputer-readable codes may be modulated into carrier signals andincluded in a communication carrier at a specific time and also bedistributed to, stored in and executed by computers connected by anetwork. The program codes for implementing the combined control logicsmay be easily inferred by programmers in the art.

All embodiments of the present disclosure may be similarly applied to acase in which the cathode has a single cathode material and the anodehas two or more anode materials. In this case, the voltage relaxationmay occur when a secondary battery comes to an idle state or a no-loadstate while being charged in an intrinsic voltage range.

In an embodiment, the anode of the secondary battery may include a firstanode material and a second anode material having different operatingvoltage ranges.

For example, when the secondary battery is in the charge mode, if thesecondary battery has a low voltage, operating ions may be mainlyintercalated into the second anode material, while if the secondarybattery has a high voltage on the contrary, operating ions may be mainlyintercalated into the first anode material. In addition, when thesecondary battery is in the discharge mode, if the secondary battery hasa high voltage, operating ions may be deintercalated from the firstanode material, while if the secondary battery has a low voltage on thecontrary, operating ions may be deintercalated from the second anodematerial.

In this case, if the state of a secondary battery in the charge modestarts increasing from 0%, operating ions are mainly intercalated intothe second anode material. In addition, if the state of the secondarybattery increases until the capacity of the second anode material towhich operating ions may be intercalated is mostly used, the resistanceof the second anode material rapidly increases, and operating ions startbeing intercalated into the first anode material. If the secondarybattery comes to an idle state or a no-load state after operating ionsare intercalated into the first anode material to some extent, apotential difference is created between the first anode material and thesecond anode material, which may cause a voltage relaxation in which theoperating ions intercalated into the first anode material aretransferred to the second anode material.

Generally, if the charging process stops, the voltage of the secondarybattery exhibit a decreasing pattern while converging toward theopen-circuit voltage. However, if a voltage relaxation occurs, thevoltage of the secondary battery converges toward the open-circuitvoltage while making a voltage profile including an inflection point.

Therefore, if a voltage profile of a secondary battery is measured whenthe secondary battery in a charge mode shifts to an idle state or ano-load state, a voltage relaxation may be identified from the voltageprofile, and optionally a state of the secondary battery may beestimated from the voltage profile by using a voltage estimating modelderived from the circuit model.

In order to identify the occurrence of a voltage relaxation, variousmethods described above may be applied. In addition, the circuit modeldescribed above may be easily changed by those skilled in the art inconsideration that blended anode materials are included in the anode ofthe secondary battery and a single cathode material is included in thecathode of the secondary battery. In other words, the circuit model usedfor deriving the voltage estimating model may be replaced with a circuitmodel including an anode material circuit unit having a first anodematerial circuit unit and a second anode material circuit unit and acathode material circuit unit, and the current flowing on each circuitunit and the voltage formed at a circuit element included in eachcircuit unit may be reinterpreted in light of charging the secondarybattery, as obvious to those skilled in the art.

Further, all embodiments of the present disclosure may also be similarlyapplied to a case in which blended cathode materials and blended anodematerials are respectively included in the cathode and the anode of thesecondary battery.

In this case, a voltage relaxation may occur in both the discharge modeand the charge mode. In other words, the voltage relaxation may occurwhen a secondary battery in the discharge mode comes to an idle state ora no-load state in a voltage range in which a voltage relaxation mayoccur or when a secondary battery in the charge mode comes to an idlestate or a no-load state in a voltage range in which a voltagerelaxation may occur.

The voltage relaxation occurring in the discharge mode or the chargemode may be detected by measuring a voltage profile of the secondarybattery. In addition, optionally, a state of the secondary battery maybe estimated from the measured voltage profile by using the voltageestimating model according to the present disclosure.

The circuit model used for deriving the voltage estimating model may bereplaced with a circuit model including an anode material circuit unithaving a first anode material circuit unit and a second anode materialcircuit unit and a cathode material circuit unit having a first cathodematerial circuit unit and a second cathode material circuit unit, andthe current flowing on each circuit unit and the voltage formed at acircuit element included in each circuit unit may be reinterpreted inlight of charging or discharging the secondary battery, as obvious tothose skilled in the art.

In various embodiments of the present disclosure, components named‘unit’ should be understood as functionally distinguishable elements andnot physically distinguishable elements. Therefore, each component maybe integrated with another component, selectively, or each component maybe divided into sub complements for efficient execution of controllogic(s). However, even though components are integrated or divided,such integrated or divided components should be interpreted as beingwithin the scope of the present disclosure if their functions arerecognized as having substantially the same identity with the presentdisclosure, as obvious to those skilled in the art.

The present disclosure has been described in detail. However, it shouldbe understood that the detailed description and specific examples, whileindicating preferred embodiments of the disclosure, are given by way ofillustration only, since various changes and modifications within thespirit and scope of the disclosure will become apparent to those skilledin the art from this detailed description.

What is claimed is:
 1. A battery system, comprising: (1) a batterymanagement system (BMS); and (2) a blended lithium secondary battery,comprising: (a) a cathode comprising a first cathode material and asecond cathode material different from the first cathode material,wherein the first and second cathode materials have different operatingvoltage ranges; (b) an anode; and (c) a separator, wherein the BMS iselectrically connected to the blended lithium secondary battery andincludes a sensor configured to measure a current and a voltage of theblended lithium secondary battery, and wherein the BMS is configured to:control the charge and discharge of the blended lithium secondarybattery in a voltage range where the blended lithium secondary batteryundergoes voltage relaxation; monitor the current and voltage of theblended lithium secondary battery during operation of the blendedlithium secondary battery according to time using the sensor; detect atwo-stage voltage relaxation from the change of voltage of the blendedlithium secondary battery during operation of the battery system,wherein the voltage relaxation includes the transfer of operating ionsbetween the first and second cathode active materials; estimate a stateof charge of the blended lithium secondary battery corresponding to thedetected two-state voltage relaxation; and update the state of charge ofthe blended lithium secondary battery based on the estimated state ofcharge.
 2. The battery system according to claim 1, wherein the BMSdetects the two-stage voltage relaxation when the occurrence of aninflection point is identified in a changing pattern of the voltage, andwherein the two-stage voltage relaxation includes two voltage risesbefore and after the inflection point.
 3. The battery system accordingto claim 2, wherein the BMS identifies the occurrence of the inflectionpoint by using a first-order differential value or a second-orderdifferential value of the voltage of the blended lithium secondarybattery with respect to time.
 4. The battery system according to claim2, wherein the BMS determines a reference parameter including a voltagecorresponding to the inflection point, a time corresponding to theinflection point, a first-order differential value with respect to timecalculated at the inflection point, a value obtained by integrating thevoltage profile between predetermined two points before and after theinflection point, a first-order differential value or second-orderdifferential value of the voltage profile calculated at a predeterminedpoint before and/or after the inflection point with respect to time, orcombinations thereof, and wherein a state of the blended lithiumsecondary battery corresponding to the determined reference parameter isestimated by using a predetermined relationship between the referenceparameter and the state of the blended lithium secondary battery.
 5. Thebattery system according to claim 4, wherein the predeterminedrelationship is a look-up table which is capable of mapping a state ofthe blended lithium secondary battery by means of at least one referenceparameter.
 6. The battery system according to claim 4, wherein thepredetermined relationship is a look-up function where at least onereference parameter and a state of the blended lithium secondary batterycorresponding thereto are respectively defined as an input parameter andan output parameter.
 7. The battery system according to claim 1, whereinthe BMS monitors the current and voltage of the blended lithiumsecondary battery when the blended lithium secondary battery comes to anidle state or a no-load state while being discharged.
 8. The batterysystem according to claim 1, wherein the first cathode material has alayered structure and the second cathode material has an olivinestructure, and wherein the first cathode material and the second cathodematerial are blended in a weight ratio of 7:3.
 9. The battery systemaccording to claim 8, wherein the first cathode material comprisesLi_(1+x)Ni_(a)Co_(b), Mn_(c)O₂ (NMC), where x>0; a=b=c=⅓, and whereinthe second cathode material comprises LiFePO₄ (LFP).